chars int64 40 24k | content_type stringclasses 9
values | id stringlengths 13 64 | source stringclasses 5
values | subset stringclasses 31
values | text stringlengths 40 24k |
|---|---|---|---|---|---|
1,623 | lean_file_chunk | 19bffd290bd3315802693bb549aa99226b9e47967f533e3accb1ac4b8bcfffe8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Algebra.Order.Ring.Basic
public import Mathlib.Algebra.Ring.Divisibility.Basic
public im... |
6,836 | lean_file_chunk | 07c416b609d496a994d9a0ed2e5dde4ca97bb8638b8cc054d2ba74bb4a5df261 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jeremy Avigad, Yury Kudryashov, Patrick Massot
-/
module
public import Mathlib.Data.Set.Finite.Lemmas
public import Mathlib.Order.Filter.Bases.Finite
public import Mat... |
6,962 | lean_file_chunk | a259092db89c85b93c170c1b20d5028559b42ad640312f92bd8b4ea41ab922c9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Algebra.Order.Monoid.OrderDual
public import Mathlib.Algebra.Order.Monoid.Unbundled.Pow
public import Mathlib.Order.Filter.AtTopBot.Te... |
4,000 | lean_file_chunk | ce3bf483d7f8cfd52b017bb83bcec5acc8b055801d63b20b40dd3f787276b45b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Algebra.Order.Ring.Defs
public import Mathlib.Order.Filter.AtTopBot.Group
/-!
# Convergence to ±infinity in ordered rings
-/
public ... |
7,590 | lean_file_chunk | 16a904d755a310a333d542f2c19872bf0bc54dad573477d9191e9ee625c1871d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jeremy Avigad, Yury Kudryashov, Patrick Massot
-/
module
public import Mathlib.Order.Filter.AtTopBot.Finite
public import Mathlib.Order.Filter.AtTopBot.Prod
public imp... |
7,499 | lean_file_chunk | 610edf7fa41993a2950528283d7984fa39bed98449d85b14b7eb0bf1760c4751 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jeremy Avigad, Yury Kudryashov, Patrick Massot
-/
module
public import Mathlib.Order.Filter.AtTopBot.Disjoint
public import Mathlib.Order.Filter.Tendsto
/-!
# Limits ... |
5,626 | lean_file_chunk | fe9608ae1b5125e0882379e023a7d3b0d6ad7bf3a7fcb847414abae883ac0940 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Algebra.Order.Group.MinMax
public import Mathlib.Order.Filter.AtTopBot.Basic
public import Mathlib.Order.Filter.AtTopBot.Map
public im... |
3,320 | lean_file_chunk | a469daed25de38dec1fbd0d2ffc3ef99fad62f3e750c59774f9fb1bc1a1baba6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck, David Loeffler
-/
module
public import Mathlib.Order.Filter.AtTopBot.Archimedean
public import Mathlib.Order.Filter.Prod
public import Mathlib.Order.Interval.Finset.De... |
4,423 | lean_file_chunk | 42f26b4657aa02ec4c73de38e2dbf03ba1eeb51c28b38ba73675d09b9eff455d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jeremy Avigad, Yury Kudryashov, Patrick Massot
-/
module
public import Mathlib.Data.Finset.Prod
public import Mathlib.Order.Filter.AtTopBot.Basic
public import Mathlib... |
12,277 | lean_file_chunk | caad5820d66ca5d50408394fbc239fdb5755e76a1d50beed65470ed8e92009bb | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Yury Kudryashov
-/
module
public import Mathlib.Algebra.Order.Archimedean.Basic
public import Mathlib.Order.Filter.AtTopBot.Group
public import Mathlib.Order.Filter.Co... |
1,582 | lean_file_chunk | 18c36d5e38fef06009f33137753bdee61fff41eac871cd609791c38d2b049b61 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jeremy Avigad, Yury Kudryashov, Patrick Massot
-/
module
public import Mathlib.Order.Filter.AtTopBot.Defs
public import Mathlib.Order.Filter.Map
public import Mathlib.... |
3,830 | lean_file_chunk | 2a777201dcb1e56c704ec9153d816a3cab2d26c6dd401584755487386eedff77 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jeremy Avigad, Yury Kudryashov, Patrick Massot
-/
module
public import Mathlib.Data.Finset.Order
public import Mathlib.Order.Filter.AtTopBot.Basic
public import Mathli... |
20,689 | lean_file_chunk | 1a1abe9ae98f7df087e1466c377cbb446ee44944a6114adf81b360cb2ab44710 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jeremy Avigad, Yury Kudryashov, Patrick Massot
-/
module
public import Mathlib.Order.Filter.Bases.Basic
public import Mathlib.Order.Filter.AtTopBot.Tendsto
public impo... |
1,656 | lean_file_chunk | 1ffeeef59368f23dc8e512e75c218959c977e87ee936b231490c8db6301e6275 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jeremy Avigad, Yury Kudryashov, Patrick Massot
-/
module
public import Mathlib.Order.Filter.AtTopBot.Defs
public import Mathlib.Order.Interval.Set.Disjoint
/-!
# Disj... |
4,714 | lean_file_chunk | 6b5d98887b71e052948aa89585ae3d2ec2f4a6bd1c486811360888603d8766c8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jeremy Avigad, Yury Kudryashov, Patrick Massot
-/
module
public import Mathlib.Data.Set.Piecewise
public import Mathlib.Order.Filter.Basic
/-!
# Definition of `Filter... |
1,057 | lean_file_chunk | 4bc4effb5716ffc1c677d91b1f49ffb6a86eddc833486607793922ff1ade88c4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yuyang Zhao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuyang Zhao
-/
module
public import Mathlib.Algebra.Order.Floor.Semiring
public import Mathlib.Algebra.Order.Ring.Abs
public import Mathlib.Order.Filter.AtTopBot.Finite
public import Mat... |
3,517 | lean_file_chunk | ad03b32bf86f878924f71cfb7a80ec60314d95d0845e0c532abb4b33a5fe20f3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Algebra.BigOperators.Group.Finset.Preimage
public import Mathlib.Order.Filter.AtTopBot.Basic
/-!
# Two lemmas about limit of `Π b ∈ s... |
16,571 | lean_file_chunk | 11a4d3336c6cec0dcc39260b19bcae1f75fea42e6ba54c556edeb45aa3e21a3b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Algebra.Field.Defs
public import Mathlib.Order.Filter.AtTopBot.Ring
/-!
# Convergence to ±infinity in linear ordered (semi)fields
-/
... |
9,517 | lean_file_chunk | f89765f48e9f586eba409c7a0af6b1994326800eb5e9517351d6630fcdcb72da | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jeremy Avigad, Yury Kudryashov, Patrick Massot
-/
module
public import Mathlib.Order.ConditionallyCompleteLattice.Indexed
public import Mathlib.Order.Filter.AtTopBot.T... |
5,119 | lean_file_chunk | a4d16f430a59140981e6b5739d4e18ced8b3d838e354e0c5968227fd5207e9e1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Johannes Hölzl, Mario Carneiro, Patrick Massot
-/
module
public import Mathlib.Order.Filter.Bases.Basic
public import Mathlib.Order.Filter.Finite
/-!
# Finiteness r... |
23,990 | lean_file_chunk | d25c0cf1f15ccccb99de0a64afe34cc26a7400e3e567fdef936bbaf2f4771308 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Johannes Hölzl, Mario Carneiro, Patrick Massot
-/
module
public import Mathlib.Data.Set.Sigma
public import Mathlib.Order.Filter.Defs
public import Mathlib.Order.Fil... |
10,539 | lean_file_chunk | da33597cad7f7c1e66f1e24b4930b56fae87a2dfba49ee59898a89cf0189e043 | lean_source_file | pkg_mathlib_source_file_chunks | Disjoint l' l ↔ ∃ i, p i ∧ (s i)ᶜ ∈ l' :=
disjoint_comm.trans h.disjoint_iff_left
theorem le_iff_forall_inf_principal_compl {f g : Filter α} : f ≤ g ↔ ∀ V ∈ g, f ⊓ 𝓟 Vᶜ = ⊥ :=
forall₂_congr fun _ _ => mem_iff_inf_principal_compl
theorem inf_neBot_iff_frequently_left {f g : Filter α} :
NeBot (f ⊓ g) ↔ ∀ {p : ... |
4,494 | lean_file_chunk | 32c5da8a15975ef547b13b752a797ffe483ad266b3ba613f09c5a89b9fa0551d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jeremy Avigad, Yury Kudryashov
-/
module
public import Mathlib.Order.Filter.Ultrafilter.Defs
public import Mathlib.Order.Filter.Cofinite
public import Mathlib.Order.Zo... |
14,206 | lean_file_chunk | a8d338da448997b5aed22b682cf90147e253548282aae768b8b3a3ed25758ebf | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jeremy Avigad, Yury Kudryashov
-/
module
public import Mathlib.Order.Filter.Map
public import Mathlib.Order.ZornAtoms
/-!
# Ultrafilters
An ultrafilter is a minimal ... |
2,440 | lean_file_chunk | dc141ffa66685c50aa64250b660cd5f779d53e56eb8b72fe1ff9dba8f1a79c43 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Jonas van der Schaaf. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jonas van der Schaaf
-/
module
public import Mathlib.ModelTheory.Types
public import Mathlib.Topology.Bases
public import Mathlib.Topology.Connected.TotallyDisconnected
public ... |
3,757 | lean_file_chunk | c30f585e39c68a6b4a37429f3bf3df0aeccca55421946a86e095761c055541f6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Dexin Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dexin Zhang
-/
module
public import Mathlib.Algebra.Group.Basic
public import Mathlib.Algebra.Module.NatInt
public import Mathlib.ModelTheory.Semantics
/-!
# Presburger arithmetic
This... |
7,567 | lean_file_chunk | dbd7bb969f8870047c4fff3f9270d86aa4d31f117400d85aee56c21bf29845df | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Dexin Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dexin Zhang
-/
module
public import Mathlib.ModelTheory.Arithmetic.Presburger.Basic
public import Mathlib.ModelTheory.Arithmetic.Presburger.Semilinear.Basic
public import Mathlib.ModelTh... |
23,949 | lean_file_chunk | 4c5f7340a72e149e8de29861e2242c3f329bfefd6a161e7c496e8562a572cb8a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Dexin Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dexin Zhang
-/
module
public import Mathlib.Data.Matrix.ColumnRowPartitioned
public import Mathlib.ModelTheory.Arithmetic.Presburger.Semilinear.Defs
import Mathlib.Algebra.Group.Submono... |
12,035 | lean_file_chunk | a5af5381f0fe1ba4d809449eab55eb590700714022afea038dfe9323b3df2775 | lean_source_file | pkg_mathlib_source_file_chunks | · rw [hs.toRatVec_fract_eq, add_sub_cancel_left]
simp [← hs.basis_apply, Finsupp.single_apply, Int.fract_lt_one]
private theorem fract_eq_self_of_mem_fundamentalDomain {x} (hx : x ∈ hs.fundamentalDomain) :
hs.fract x = x := by
rw [← toRatVec_inj, hs.toRatVec_fract_eq]
conv_lhs =>
enter [2, 2, i]
rw... |
19,356 | lean_file_chunk | c87e855c68e7ef2af8e8fb6b85a1ff4cd855f647b771d252c649ea4edbb9cb6c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Dexin Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dexin Zhang
-/
module
public import Mathlib.GroupTheory.Finiteness
public import Mathlib.LinearAlgebra.LinearIndependent.Defs
public import Mathlib.Algebra.Order.Group.Nat
import Mathli... |
10,475 | lean_file_chunk | 8f99ded1bac461c59efd07ffe5048272e18b7c9195a7a7d1015e8b7f5daf2997 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
module
public import Mathlib.Data.Nat.PrimeFin
public import Mathlib.FieldTheory.IsAlgClosed.AlgebraicClosure
public import Mathlib.FieldTheory.IsAlgClosed.Classificatio... |
3,393 | lean_file_chunk | 19bad513e592459e1252446371dbedae6e99c8e61a3114adc4c92f8237bb5e35 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
module
public import Mathlib.Algebra.CharP.Basic
public import Mathlib.ModelTheory.Algebra.Ring.FreeCommRing
public import Mathlib.ModelTheory.Algebra.Field.Basic
/-!
#... |
5,950 | lean_file_chunk | c352482b9f9c4920d06396c7c85f255a829b8201cdd61683c7f0128d10ed9432 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
module
public import Mathlib.ModelTheory.Syntax
public import Mathlib.ModelTheory.Semantics
public import Mathlib.ModelTheory.Algebra.Ring.Basic
public import Mathlib.Al... |
12,056 | lean_file_chunk | a2f42030eb018d16a5b3ae0afef4273854f63fbe5248ed0c56593e777c97fe45 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
module
public import Mathlib.ModelTheory.Syntax
public import Mathlib.ModelTheory.Semantics
public import Mathlib.Algebra.Ring.Equiv
/-!
# First-Order Language of Rings... |
2,064 | lean_file_chunk | cb4c7dd46b1153325f226f2fdac7bdf5a15bde33f6994ceca2e7765e3fd6d278 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
module
public import Mathlib.ModelTheory.Algebra.Ring.Basic
public import Mathlib.RingTheory.FreeCommRing
/-!
# Making a term in the language of rings from an element o... |
1,462 | lean_file_chunk | be068bd50196905255ce48ed1590dd3649364b7f7e6cdcc1efb08d66cb51033f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
module
public import Mathlib.ModelTheory.Definability
public import Mathlib.RingTheory.MvPolynomial.FreeCommRing
public import Mathlib.RingTheory.Nullstellensatz
public ... |
23,996 | lean_file_chunk | 66fe8b846966a5e3972438bc922decf82036a4a881677b98bd6b06679c50c564 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Patrick Massot
-/
module
public import Mathlib.Topology.Order
public import Mathlib.Topology.NhdsSet
/-!
# Specific classes of maps between topologica... |
11,352 | lean_file_chunk | 9a602eed9e0c748c1fe5a3876b1037eda5605228d75224ae9c5ea72151d1a68a | lean_source_file | pkg_mathlib_source_file_chunks | simp_rw [Filter.le_def, mem_comap'', ← subset_interior_iff_mem_nhdsSet,
← subset_kernImage_iff, isClosedMap_iff_kernImage_interior]
exact ⟨fun H s t hst ↦ hst.trans H, fun H s ↦ H _ subset_rfl⟩
alias ⟨IsClosedMap.comap_nhdsSet_le, _⟩ := isClosedMap_iff_comap_nhdsSet_le
theorem isClosedMap_iff_comap_nhds_le :
... |
5,955 | lean_file_chunk | 467c72ce982bd79c542055ea7849014dc3584ba5d08ec8cbdeaa8ad404946e9d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Topology.Maps.Basic
public import Mathlib.Topology.Baire.Lemmas
/-!
# Open quotient maps
An open quotient map is an open map `f : X ... |
1,624 | lean_file_chunk | bcd6ec060a2f2f102b56d51a4c0d03512909df9c4f305e962454b5a5e1e99316 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Xavier Roblot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Xavier Roblot
-/
module
public import Mathlib.Topology.Order.OrderClosed
public import Mathlib.Topology.LocallyClosed
/-!
# Intervals are locally closed
We prove that the intervals o... |
16,736 | lean_file_chunk | e6e7556a0f1f18245d3f6605877560f71b7c7faf1290c0b21973e975d82e570d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Heather Macbeth
-/
module
public import Mathlib.Topology.Homeomorph.Defs
public import Mathlib.Topology.Order.LeftRightNhds
/-!
# Continuity of monotone functions
... |
20,722 | lean_file_chunk | 11b8ed295c1ec2badf1758d5d11a48cae5321a4edf72ec2cb42526cb471f6698 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Christopher Hoskin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christopher Hoskin
-/
module
public import Mathlib.Order.Hom.CompleteLattice
public import Mathlib.Topology.Homeomorph.Defs
public import Mathlib.Topology.Order.Lattice
/-!
# Low... |
12,069 | lean_file_chunk | 9ebb21aeb22b1e6adac2212d28a90e1556f588db6f99d05fe331e11c13cac1d8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne, Sébastien Gouëzel
-/
module
public import Mathlib.Topology.Order.Basic
public import Mathlib.Data.Fintype.WithTopBot
/-! # Order topology on `WithTop ι`
When `ι` is a to... |
13,020 | lean_file_chunk | 848212e333de5cb86b6956c5e3431deb524fcba2673ecc43e7403d95cdf4bde5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Yury Kudryashov
-/
module
public import Mathlib.Topology.Order.IsLUB
/-!
# Order topology on a densely ordered set
-/
@[expose] public section
open ... |
1,573 | lean_file_chunk | 02c807395eccdeff746fd23693669243c7a9b08b3966c7ea507abeab2159e42c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Bjørn Kjos-Hanssen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bjørn Kjos-Hanssen, Patrick Massot
-/
module
public import Mathlib.Topology.Order.OrderClosed
public import Mathlib.Topology.Order.LocalExtr
/-!
# Local maxima from monotonicity ... |
8,601 | lean_file_chunk | 57ff71e1662bb2eae476ec0f3ab5a559ea2a6f91b6aa87a50df5e19511d59b44 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Topology.Order.Basic
public import Mathlib.Order.SuccPred.Limit
import Mathlib.Topology.Order.LeftRightNhds
/-!
# `Filter.atTop` and ... |
3,382 | lean_file_chunk | edcc30c40a38e721277668acbdfc91f829fe265f9dbca7648f6a1269a05fc811 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux, Violeta Hernández Palacios
-/
module
public import Mathlib.Topology.Order.Basic
public import Mathlib.Order.SuccPred.Limit
/-!
# Order topologies of successor or predec... |
4,171 | lean_file_chunk | 9d98c1aa42c3772a0e7f5503f544758d3d3f6a5989de6b76cccef43f8aa1262a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Topology.Bornology.Constructions
/-!
# Bornology of order-bounded sets
This file relates the notion of bornology-boundedness (sets that li... |
23,999 | lean_file_chunk | 53214ce11586b7962a0695a937ec44131bcd7fc74ad51e40a71a9271c26d7e36 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Yury Kudryashov
-/
module
public import Mathlib.Topology.Algebra.Support
public import Mathlib.Topology.Order.IntermediateValue
public import Mathlib.Topology.Order.Is... |
1,733 | lean_file_chunk | 0f9f3759a2f20888d0fb91f178b19beef7fa75c915257a443f94aedd6e0099bc | lean_source_file | pkg_mathlib_source_file_chunks | theorem image_Icc (hab : a ≤ b) (h : ContinuousOn f <| Icc a b) :
f '' Icc a b = Icc (sInf <| f '' Icc a b) (sSup <| f '' Icc a b) :=
eq_Icc_of_connected_compact ⟨(nonempty_Icc.2 hab).image f, isPreconnected_Icc.image f h⟩
(isCompact_Icc.image_of_continuousOn h)
theorem image_uIcc_eq_Icc (h : ContinuousOn f ... |
15,997 | lean_file_chunk | 5e48535bc1cc235137ea7a9f9355193093f41e964bcccb4fdf434a7db274904b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Christopher Hoskin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christopher Hoskin
-/
module
public import Mathlib.Order.DirSupClosed
public import Mathlib.Order.ScottContinuity
public import Mathlib.Topology.Order.UpperLowerSetTopology
/-!
#... |
2,907 | lean_file_chunk | 67ed9107e648a9e8bfbcc8c95c1395e1f56799143bf97aa653e16a052a0c2480 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Topology.Order.Basic
public import Mathlib.Order.Filter.CountableSeparatingOn
/-!
# Countably many infinite intervals separate points... |
4,377 | lean_file_chunk | 486233cf672b2b3cea8c48cb22acfcefc453bb82eb02dce1305df2bc499716a7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Order.Interval.Set.OrdConnectedComponent
public import Mathlib.Topology.Order.Basic
public import Mathlib.Topology.Separation.Regular
... |
2,260 | lean_file_chunk | 5c16f491cbabd29d365f8c7d9014d69af77cd692cf61bb92b002b8bd957304de | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Topology.Order.OrderClosed
public import Mathlib.Topology.Order.LocalExtr
/-!
# Maximum/minimum on the closure of a set
In this file... |
23,996 | lean_file_chunk | 3ff01b16f9a0323396fedbc18f7e3ab7269dff46099e2e1334b104d2dcb9e2cf | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Yury Kudryashov, Yaël Dillies
-/
module
public import Mathlib.Order.Filter.CountableInter
public import Mathlib.Order.LiminfLimsup
public import Mathli... |
8,556 | lean_file_chunk | 9feeae9b6c356937a2750e04d6bdb553e580981853decd7cd075e4f72caf8955 | lean_source_file | pkg_mathlib_source_file_chunks | using Antitone.isCoboundedUnder_ge_of_isCobounded f_decr cobdd
· rcases hd with ⟨e, ⟨he, fe_eq_d⟩⟩
filter_upwards [he] with x hx using (fe_eq_d.symm ▸ f_decr hx)
· by_cases! h' : ∃ c, c < F.limsSup ∧ Set.Ioo c F.limsSup = ∅
· rcases h' with ⟨c, c_lt, hc⟩
have B : ∃ᶠ n in F, F.limsSup ≤ n := by
... |
23,995 | lean_file_chunk | 63e70e3fbc36dd46ee85187d90b37d509151002b6d2da8a61dc1227aa7b03622 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Alistair Tucker, Wen Yang
-/
module
public import Mathlib.Order.Interval.Set.Image
public import Mathlib.Order.CompleteLatticeIntervals
public import Mathlib.Topolog... |
18,030 | lean_file_chunk | 43442ff97d79b222217a912e1d8cafc715d9498abb1a33e79b4089724f6f3f2f | lean_source_file | pkg_mathlib_source_file_chunks | ordConnected_Ioo.isPreconnected
theorem isPreconnected_uIoo : IsPreconnected (uIoo a b) :=
isPreconnected_Ioo
theorem isPreconnected_Ioc : IsPreconnected (Ioc a b) :=
ordConnected_Ioc.isPreconnected
theorem isPreconnected_uIoc : IsPreconnected (uIoc a b) :=
isPreconnected_Ioc
theorem isPreconnected_Ico : IsPr... |
23,959 | lean_file_chunk | cd726eddb5e310f55a8dfd9fa8dfac3c808950ab405fa57786af29da354f2b35 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Yury Kudryashov
-/
module
public import Mathlib.Order.Filter.Interval
public import Mathlib.Order.Interval.Set.Pi
public import Mathlib.Order.OrdContin... |
20,250 | lean_file_chunk | dc36952f1405641d5264d7ddf4cc1041922595f7891c98cbbf2e48620af90c32 | lean_source_file | pkg_mathlib_source_file_chunks | rcases eq_empty_or_nonempty (Ioo a b) with (H | ⟨c, hac, hcb⟩)
· have : Ico a b = Icc a a := by rw [← Icc_union_Ioo_eq_Ico le_rfl hab, H, union_empty]
exact ⟨a, le_rfl, this ▸ ⟨Ico_mem_nhdsGE hab, hbs⟩⟩
· refine ⟨c, hac.le, Icc_mem_nhdsGE hac, ?_⟩
exact (Icc_subset_Ico_right hcb).trans hbs
theorem ... |
2,750 | lean_file_chunk | d09de13c5039dd3910e2e293eaf0b088ff8d1f05e3aab042ca6bec1ef6e9200a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Order.UpperLower.Basic
public import Mathlib.Topology.Connected.TotallyDisconnected
/-!
# Priestley spaces
This file defines Priestley spa... |
2,435 | lean_file_chunk | 96d3879888515221e9fb0715da6dfabe605a8d933d2d87d6c1198f3b74605b5a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Patrick Massot
-/
module
public import Mathlib.Order.Interval.Set.ProjIcc
public import Mathlib.Topology.Order.Basic
/-!
# Projection onto a closed interval
In thi... |
2,918 | lean_file_chunk | 5d594130d273f77f2e5ff60022449f1b3e909cf6376ad19ba3a0b7e229481028 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Topology.Order.Lattice
public import Mathlib.Order.PartialSups
/-!
# Continuity of `partialSups`
In this file we prove that `partial... |
22,518 | lean_file_chunk | 7f6f45369c74a05b443de40e74e96aac5eb5ef190b7f74e0c9b3bba79ef4ce6c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Yury Kudryashov
-/
module
public import Mathlib.Topology.Order.LeftRightNhds
/-!
# Properties of LUB and GLB in an order topology
-/
public section
... |
2,096 | lean_file_chunk | d15d47dcc647eb58ad49ca6287d2cb28940c4f74332de8eb2b9a82a090a40333 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Violeta Hernández Palacios. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Violeta Hernández Palacios
-/
module
public import Mathlib.Order.IsNormal
public import Mathlib.Topology.Order.IsLUB
/-!
# A normal function is strictly monotone and cont... |
1,255 | lean_file_chunk | 948aecd103f33e197343dcde840ce01785720ed083498c8453fde620336bcf2a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Topology.Filter
public import Mathlib.Topology.Order.Basic
/-!
# Topology on filters of a space with order topology
In this file we ... |
23,984 | lean_file_chunk | e184bd90b825c4c1d069480634a2019a3bb53ac3c8cad40ab8291788f3445420 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Yury Kudryashov
-/
module
public import Mathlib.Topology.Order.LeftRight
public import Mathlib.Topology.Separation.Hausdorff
/-!
# Order-closed topolo... |
4,746 | lean_file_chunk | dbf682752ec9136ef7a42c6e69c5ece234771b665fb18b1c717098fffc70a197 | lean_source_file | pkg_mathlib_source_file_chunks | theorem frontier_Iic_subset (a : α) : frontier (Iic a) ⊆ {a} :=
frontier_le_subset_eq (@continuous_id α _) continuous_const
@[to_dual (reorder := f g, hf hg) frontier_gt_subset_eq]
theorem frontier_lt_subset_eq (hf : Continuous f) (hg : Continuous g) :
frontier { b | f b < g b } ⊆ { b | f b = g b } := by
simpa... |
6,116 | lean_file_chunk | d4ade122d6c038309407ffeb1098b755bd21016e84fc672f7f20af974d3d85cc | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker
-/
module
public import Mathlib.Order.Antichain
public import Mathlib.Topology.ContinuousOn
public import Mathlib.Order.Interval.Set.UnorderedInterval
/-!
# Left a... |
19,595 | lean_file_chunk | 857d09c260009f0e98c5e0a4b863c06278acaadfb5fa9f150ef5954b229f2896 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
module
public import Mathlib.Topology.Order.LeftRight
public import Mathlib.Topology.Order.Monotone
public import Mathlib.Topology.Separation.Regular
/-!
# Le... |
8,804 | lean_file_chunk | 7b65b3f77871ba4c93381d2ae4516fa5ae73995da7c1614b4227a597a8288c94 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Christopher Hoskin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christopher Hoskin
-/
module
public import Mathlib.Topology.Order.LowerUpperTopology
public import Mathlib.Topology.Order.ScottTopology
/-!
# Lawson topology
This file introduce... |
15,546 | lean_file_chunk | 0234fe98d2dc0bd4fc49a79ef3d52d13a79e8666666600d96287e5680a384341 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth, Yury Kudryashov
-/
module
public import Mathlib.Topology.Order.Basic
/-!
# Bounded monotone sequences converge
In this file we prove a few theorems of the form “if... |
7,592 | lean_file_chunk | 4cb9b6fb6ca94757553c9b4d3e5e7341560217ec588532eede349c1da6fcbafb | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Topology.Order.Basic
/-!
# Set neighborhoods of intervals
In this file we prove basic theorems about `𝓝ˢ s`,
where `s` is one of th... |
18,434 | lean_file_chunk | c9a60ae0f82acd9de49b4e9fe6bfde053e0cf33f5f6abf79ba00663e938742e1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Christopher Hoskin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christopher Hoskin
-/
module
public import Mathlib.Logic.Lemmas
public import Mathlib.Topology.AlexandrovDiscrete
public import Mathlib.Topology.ContinuousMap.Basic
public import ... |
20,881 | lean_file_chunk | 8d7c253b1cd282b603b72d20ef665f9392d4a44942b5b3cc4c4acaa9bbee4dd6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Yury Kudryashov
-/
module
public import Mathlib.Order.Filter.AtTopBot.CompleteLattice
public import Mathlib.Order.Filter.AtTopBot.Group
public import M... |
23,960 | lean_file_chunk | 14e3f1194f68828a53972f95eb965c074f7a10eff7d48683710a2295bae814f8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Yury Kudryashov
-/
module
public import Mathlib.Tactic.Order
public import Mathlib.Topology.Order.IsLUB
/-!
# Monotone functions on an order topology
... |
2,994 | lean_file_chunk | 75a0348be956382df33b3111435b6de60fc2b55644f901b156fefbdf14cd650c | lean_source_file | pkg_mathlib_source_file_chunks | MonotoneOn.tendsto_nhdsLT (Mf.monotoneOn _) (Mf.map_bddAbove bddAbove_Iio)
/-- A monotone map has a limit to the right of any point `x`, equal to `sInf (f '' (Ioi x))`. -/
theorem Monotone.tendsto_nhdsGT {α β : Type*} [LinearOrder α] [TopologicalSpace α] [OrderTopology α]
[ConditionallyCompleteLinearOrder β] [Topo... |
15,769 | lean_file_chunk | 110498c3f0a203fe5105ba92b88bc20a6153cfa46a583cc6dd988ff7708356c0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Christopher Hoskin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christopher Hoskin
-/
module
public import Mathlib.Topology.Constructions
public import Mathlib.Topology.Order.OrderClosed
/-!
# Topological lattices
In this file we define mixi... |
8,614 | lean_file_chunk | 980f52d91c10c64398c63a65c4433b45515310ce47083b1cd55fe2c91a97a6b2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Christopher Hoskin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christopher Hoskin
-/
module
public import Mathlib.Data.Set.Subset
public import Mathlib.Order.Irreducible
public import Mathlib.Topology.Order.LowerUpperTopology
public import Ma... |
6,141 | lean_file_chunk | 04d35ca6dcc294a99c9795120e0ecc158b19f61b8ded312078200335cc3d3739 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Topology.Order.ExtendFrom
public import Mathlib.Topology.Order.Compact
public import Mathlib.Topology.Order.LocalExtr
public import Ma... |
20,749 | lean_file_chunk | 0d0a9b49ceb739e912675f264df17390de62fe5a2fee59b5edb340a9085cbff4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Order.Filter.Extr
public import Mathlib.Topology.ContinuousOn
/-!
# Local extrema of functions on topological spaces
## Main definit... |
3,483 | lean_file_chunk | c5497585c9aa753f259a93ba40f6dde4aaea265bfdd0fac7b134d61e90fde68a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Yury Kudryashov
-/
module
public import Mathlib.Topology.ExtendFrom
public import Mathlib.Topology.Order.DenselyOrdered
/-!
# Lemmas about `extendFrom... |
1,774 | lean_file_chunk | 19c8906c4dc6166bdb10160e9442acb40998fc7ed73228efc96f2fb6481a2d68 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
module
public import Mathlib.Data.EReal.Basic
public import Mathlib.Topology.Order.T5
/-!
# The reals are equipped with their order topology
This f... |
9,621 | lean_file_chunk | 16ad85894262d17f2d3beadfd99aedad7ed6a585ba3000a62128a0b926470acd | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
module
public import Mathlib.Topology.OpenPartialHomeomorph.IsImage
/-!
# Partial homeomorphisms: composition
## Main definitions
* `OpenPartialHomeomorph.tr... |
11,972 | lean_file_chunk | bc31646cdc2b000d8efd5c28f3a2cf02d1fa39fdc1b6165b21e2b92e3a43eb2b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
module
public import Mathlib.Topology.Homeomorph.Lemmas
public import Mathlib.Topology.OpenPartialHomeomorph.Defs
public import Mathlib.Topology.Sets.Opens
/-!... |
18,581 | lean_file_chunk | 8230fb6c2f3a2a33e74f5e0a0e000d1a279220a2a6c362f1c28e3c2f65e560d6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
module
public import Mathlib.Topology.OpenPartialHomeomorph.Composition
/-!
# Constructions of new partial homeomorphisms from old
## Main definitions
* `Ope... |
9,897 | lean_file_chunk | 120b30be0459698a417a74dfe4626519511e5c0d00ee3b3c018443fdd390c97d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
module
public import Mathlib.Topology.OpenPartialHomeomorph.Basic
/-!
# Partial homeomorphisms and continuity
## Main theorems
* `OpenPartialHomeomorph.map_n... |
8,943 | lean_file_chunk | b4872a23f633fa861fda3f732fefb3184b911c4d54f32f558b37539a82c21213 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
module
public import Mathlib.Logic.Equiv.PartialEquiv
public import Mathlib.Topology.ContinuousOn
/-!
# Partial homeomorphisms: definitions
This file defines... |
15,149 | lean_file_chunk | eeda2e6eb871a71eb33b43044ede2e1b23f9f5da49f37f1bbafc65ef2f7da34a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
module
public import Mathlib.Topology.OpenPartialHomeomorph.Continuity
/-!
# Partial homeomorphisms: Images of sets
## Main definitions
* `OpenPartialHomeomo... |
3,097 | lean_file_chunk | 9d02fa74b66a7fddeb656bbea7afac728a5478f8f2b10ee0d1971783370956dc | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Topology.Hom.ContinuousEvalConst
public import Mathlib.Topology.ContinuousMap.Defs
/-!
# Bundled maps with evaluation continuous in b... |
3,593 | lean_file_chunk | 7fe94e4c4987e81ca8d1c1ffda8eb93d585f7daf15376376cd9e2dfa67def397 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Topology.Constructions
/-!
# Bundled morphisms with continuous evaluation at a point
In this file we define a typeclass
saying that ... |
4,180 | lean_file_chunk | 4c9ebc29b74fe770672081e99653427ed8148ed05ae544d6c4e622eb0beef5ff | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Topology.ContinuousMap.Basic
/-!
# Continuous open maps
This file defines bundled continuous open maps.
We use the `DFunLike` design, so ... |
23,743 | lean_file_chunk | 14196595ef50e3359dc554c69e10ff9df762cc96a6885ea82de6958c4bdcbe29 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
module
public import Mathlib.Algebra.Notation.Indicator
public import Mathlib.Topology.Connected.LocallyConnected
public import Mathlib.Topology.Sets.Closeds
/-!
# ... |
16,505 | lean_file_chunk | e54c6f7426d3a5f5ba79f5ee568c933bdc780d27d239b7b2268eb7a49ac64b5f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
module
public import Mathlib.Algebra.Algebra.Pi
public import Mathlib.Algebra.GroupWithZero.Indicator
public import Mathlib.LinearAlgebra.Pi
public import Mathlib.To... |
3,061 | lean_file_chunk | c72a08e13e431602a60a927853a0556afb4a913275e9795b984747e637c75378 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
module
public import Mathlib.CategoryTheory.Elementwise
public import Mathlib.Topology.Sequences
public import Mathlib.Topology.Instances.Discrete
public import ... |
3,777 | lean_file_chunk | be7d4e160eab7a0af7c3a3e05f086e0657a8c38f0c690c06f4a9e6e9d69eb58d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
module
public import Mathlib.Topology.Compactness.CompactlyGeneratedSpace
public import Mathlib.CategoryTheory.Elementwise
/-!
# Compactly generated topological... |
984 | lean_file_chunk | 45ad8b9d7bfacbeaac675808bdc61c56a4c9eb1c693898817e477c71667b9e62 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.CategoryTheory.ConcreteCategory.Basic
public import Mathlib.Topology.Bornology.Hom
/-!
# The category of bornologies
This defines `Born`, ... |
3,663 | lean_file_chunk | 72bb7c5c5038fab56e2677de2684982e2fb0af8c1a2c9f9e4437fe1f53d1194a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.Algebra.Category.Ring.Basic
public import Mathlib.Topology.Category.TopCat.Basic
public import Mathlib.Topology.Algebra.Ring.Basic
/-!
# Ca... |
2,505 | lean_file_chunk | e98d0c023a5833fc9dcd7f612752dfdb138a3d829fdec9ccd3d1dc5892b2898b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
module
public import Mathlib.CategoryTheory.FintypeCat
public import Mathlib.Topology.Category.TopCat.Basic
/-!
# Category of finite topological spaces
Definit... |
9,436 | lean_file_chunk | 4e2b7f8280f95d490c76fb3923d31bc578050a7d39798affff27f5444716f2cf | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton, Patrick Massot, Kim Morrison
-/
module
public import Mathlib.CategoryTheory.Adjunction.Reflective
public import Mathlib.CategoryTheory.Monad.Limits -- shake: keep (used in... |
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