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 |
|---|---|---|---|---|---|
4,852 | lean_file_chunk | af1c3c166dca8c8a6486061225ed9d58c30464471ed254625561ac94b343a700 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
module
public import Mathlib.Topology.Sets.Opens
/-!
# Open covers
We define `IsOpenCover` as a predicate on indexed families of open sets in a topological space `... |
17,745 | lean_file_chunk | cc671a03f101f6b60d4f746b20e05a0183e1f5836659e53f67cd45f8db5ab6ee | 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, Floris van Doorn
-/
module
public import Mathlib.Order.Hom.CompleteLattice
public import Mathlib.Topology.Compactness.Bases
public import Mathlib.Topol... |
23,972 | lean_file_chunk | a5763cd8ed8b8d11c7a93f9ce95136e65c5fe1ad5029c5bfe6270b335dbffed4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Attila Gáspár. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Attila Gáspár
-/
module
public import Mathlib.Topology.Order.Lattice
public import Mathlib.Topology.Sets.Compacts
/-!
# Vietoris topology
This file defines the Vietoris topology on t... |
10,058 | lean_file_chunk | 96588cedd282a1367ca64cdbf2e7594a50b99867519f1aa7fcf672039d659eee | lean_source_file | pkg_mathlib_source_file_chunks | choose! M hM hML hMU hMK using fun U (hU : U ∈ u) =>
show ∃ M : Set α, IsCompact M ∧ M ⊆ L ∧ M ⊆ U ∧ (↑K ∩ interior M).Nonempty by
obtain ⟨x, hxK, hxU⟩ := hKu₂ U hU
obtain ⟨M, hM, _⟩ := exists_compact_subset (U := U ∩ interior L)
((hu₂ U hU).inter isOpen_interior) ⟨hxU, hLK hxK⟩
exact ⟨M, ... |
9,231 | lean_file_chunk | 940c395f9c1f6c017217e822a340ce8169ff62955e895b4fa3f546026872d45c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
module
public import Mathlib.Data.Finite.Sigma
public import Mathlib.Topology.Spectral.Prespectral
/-!
# Compact open covered sets
In this file we define the n... |
2,469 | lean_file_chunk | 0efc72581e04822c4d588a37b067f5b380fc225aa015ea58f71d8db019f6fa1a | 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.Sets.Closeds
/-!
# Clopen upper sets
In this file we define the type of clopen upper sets.
-/
@[expose] public section
open Se... |
23,999 | lean_file_chunk | d8c36ed2a72b57f431d7f607773d98df76ed6dd1534db30123d07e2d8e4c1d1d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Yaël Dillies
-/
module
public import Mathlib.Topology.Sets.Closeds
public import Mathlib.Topology.QuasiSeparated
/-!
# Compact sets
We define a few types of comp... |
4,354 | lean_file_chunk | c301639466e0c7675278877652d935fe3c418482cd2a2cbfdfb20fdb2d532a09 | lean_source_file | pkg_mathlib_source_file_chunks | @[simp, norm_cast] lemma coe_sup (s t : CompactOpens α) : ↑(s ⊔ t) = (s ∪ t : Set α) := rfl
@[simp, norm_cast] lemma coe_bot : ↑(⊥ : CompactOpens α) = (∅ : Set α) := rfl
instance : SemilatticeSup (CompactOpens α) :=
fast_instance% SetLike.coe_injective.semilatticeSup _ .rfl .rfl coe_sup
instance : OrderBot (Compact... |
18,545 | lean_file_chunk | 3ddf31fb7e101285e682e0792feb3088258989143c479c2fbf40d5366f352961 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Yaël Dillies
-/
module
public import Mathlib.Topology.Sets.Opens
public import Mathlib.Topology.Clopen
/-!
# Closed sets
We define a few types of closed sets in ... |
13,549 | lean_file_chunk | fe599ee6e95e9a734ccf87641556146ed955a1c0ef91bff35dfd362f7dcafccc | 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, Yury Kudryashov
-/
module
public import Mathlib.Order.Filter.CountableInter
public import Mathlib.Topology.Defs.Induced
public import Mathlib.Data.Set.Notation
i... |
2,268 | lean_file_chunk | 7e8aeb9bd08ee57123a68a54316703ec7ca892bfe391e82d49b3a483d06a9261 | 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, Yury Kudryashov, Aaron Liu
-/
module
public import Mathlib.Topology.Metrizable.Basic
public import Mathlib.Topology.Separation.GDelta
/-!
# `Gδ` sets and metriz... |
8,099 | lean_file_chunk | a246086b6a88bd1e9220f6ef152093c72e0759419eac524cd986eb819d536351 | 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.Topology.Continuous
public import Mathlib.Topology.NhdsSet
/-!
# Separated neighbourhoods
This file defines the predic... |
1,679 | lean_file_chunk | 9c70272b604b30287e68c4b7bdd783f5ed5bb4f8ddd565ed49d2afb21281b9db | 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.Order.Filter.CountableSeparatingOn
public import Mathlib.Topology.Separation.Basic
/-!
# Countable separating families of sets in top... |
23,992 | lean_file_chunk | fac8b9ef2d90634bcfc78a410db25eebfc55c393e2391cc40cadbb47e12032e7 | 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.Tactic.StacksAttribute
public import Mathlib.Topology.Compactness.Lindelof
public import Mathlib.Topology.Separation.Hau... |
13,557 | lean_file_chunk | db07093f87d8184867ba0b1122265524e4889270406d0a96e9a6f9ce5e375c6e | lean_source_file | pkg_mathlib_source_file_chunks | normal _ _ hcl kcl hkdis :=
hasSeparatingCovers_iff_separatedNhds.mp
⟨hcl.HasSeparatingCover kcl hkdis, kcl.HasSeparatingCover hcl (Disjoint.symm hkdis)⟩
instance (priority := 100) NormalSpace.of_regularSpace_secondCountableTopology
[RegularSpace X] [SecondCountableTopology X] : NormalSpace X :=
of_regul... |
5,219 | lean_file_chunk | 66359c937b269a8ea7122d4d95878dbb6eeb777284b834bd4916396efcf6905d | 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.Topology.Compactness.Lindelof
public import Mathlib.Topology.Compactness.SigmaCompact
public import Mathlib.Topology.Ins... |
1,484 | lean_file_chunk | d0facf451ec908003bb12e68fc9b6f8a887e8050b7eb5148374bf721d5a56fa2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Bryan Wang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Geoffrey Irving, Bryan Wang, Oliver Nash
-/
module
public import Mathlib.Topology.GDelta.MetrizableSpace
public import Mathlib.Topology.Separation.CompletelyRegular
public import Mathlib.... |
1,169 | lean_file_chunk | 756545c273ccb130ff70721cb58151478d46d0b8ab2c6e7ce4b9d40113f6429c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Miyahara Kō. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Miyahara Kō
-/
module
public import Mathlib.Topology.Order.UpperLowerSetTopology
public import Mathlib.Topology.Separation.Regular
/-!
# Linear upper or lower sets topologies are comple... |
23,971 | lean_file_chunk | 77844f97065dfb545c01e3ca191b0e96bc27e3f7120a96111113a43b01524538 | 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.Algebra.Notation.Support
public import Mathlib.Topology.Inseparable
public import Mathlib.Topology.Piecewise
public impo... |
23,967 | lean_file_chunk | 6f79452baa176719815be99e0424b86414eee9743965e61958a6403166f93d01 | lean_source_file | pkg_mathlib_source_file_chunks | (t1Space_iff_t0Space_and_r0Space.mp ‹T1Space X›).left
@[simp]
theorem compl_singleton_mem_nhds_iff [T1Space X] {x y : X} : {x}ᶜ ∈ 𝓝 y ↔ y ≠ x :=
isOpen_compl_singleton.mem_nhds_iff
theorem compl_singleton_mem_nhds [T1Space X] {x y : X} (h : y ≠ x) : {x}ᶜ ∈ 𝓝 y :=
compl_singleton_mem_nhds_iff.mpr h
theorem clos... |
5,964 | lean_file_chunk | 049653b1eaabf0c22a7ecff16370d5b29722279a15706bd6d4ea1267c2a7d625 | lean_source_file | pkg_mathlib_source_file_chunks | theorem Topology.IsInducing.r1Space [TopologicalSpace Y] {f : Y → X} (hf : IsInducing f) :
R1Space Y := .of_continuous_specializes_imp hf.continuous fun _ _ ↦ hf.specializes_iff.1
protected theorem R1Space.induced (f : Y → X) : @R1Space Y (.induced f ‹_›) :=
@IsInducing.r1Space _ _ _ _ (.induced f _) f (.induced... |
670 | lean_file_chunk | edb880db09ba7ee2853c6fe0b35b8c82ab6790e8ca4b598c254fbbb92b23aa79 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Miyahara Kō. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Miyahara Kō
-/
module
public import Mathlib.Topology.Separation.Basic
public import Mathlib.Topology.AlexandrovDiscrete
/-!
# T1 Alexandrov-discrete topology is discrete
-/
@[expose] p... |
23,914 | lean_file_chunk | 5a18259b89d27963d310f80ea8ddf6d4514ad98e359a384503387be0158d3c4e | 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.Topology.Compactness.SigmaCompact
public import Mathlib.Topology.Irreducible
public import Mathlib.Topology.Separation.B... |
9,999 | lean_file_chunk | d0248d5356d4d9c4c7b09a54dc34bdde6ded7bbba0690d67fd4da84eb0ee09b4 | lean_source_file | pkg_mathlib_source_file_chunks | /-- If `f x = g x` for all `x ∈ s` and `f`, `g` are continuous on `t`, `s ⊆ t ⊆ closure s`, then
`f x = g x` for all `x ∈ t`. See also `Set.EqOn.closure`. -/
theorem Set.EqOn.of_subset_closure [T2Space Y] {s t : Set X} {f g : X → Y} (h : EqOn f g s)
(hf : ContinuousOn f t) (hg : ContinuousOn g t) (hst : s ⊆ t) (hts... |
11,029 | lean_file_chunk | f70af436fb1ea8c0b93dca2a37ecba28d33db6bb33ef449c8aab8c3d18cdf4a1 | 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.Fintype.Option
public import Mathlib.Topology.Separation.Regular
public import Mathlib.Topology.Connected.TotallyDi... |
11,867 | lean_file_chunk | 2057e508fc7633683f72995c491111400a46ee1d595f354b984d0b9009351c6a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Matias Heikkilä. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Matias Heikkilä
-/
module
public import Mathlib.Topology.UrysohnsLemma
public import Mathlib.Topology.UnitInterval
public import Mathlib.Topology.Compactification.StoneCech
public im... |
9,155 | lean_file_chunk | 85606f6e99697e5dc5136adf881db73496a62cbba91b25c4d7aebabfa8eb80f5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
module
public import Mathlib.Algebra.Notation.Indicator
public import Mathlib.Data.Fintype.BigOperators
public import Mathlib.Order.Disjointed
public import Mathlib.... |
2,102 | lean_file_chunk | dd93da33274f85d0be35255ae0779eb562620b8cefdcca2aa744d6b281960b22 | 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.Topology.Separation.Basic
public import Mathlib.Topology.Connected.TotallyDisconnected
/-!
# Interaction of separation ... |
3,261 | lean_file_chunk | 00017830e3efc2be097c2663b688f61b993b99fda350295252c8d7f76aecb52b | 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, Tian Chen
-/
module
public import Mathlib.SetTheory.Cardinal.Continuum
public import Mathlib.Topology.Separation.Regular
/-!
# Not normal topological spaces
In thi... |
3,012 | lean_file_chunk | 7e61f1308a4b149a4bbcfc4c0d007e826fc4e6d73a0335cfd2a63ba36279ef48 | 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.Constructions.SumProd
/-!
# Maps equivariantly-homeomorphic to projection in a product
This file contains the definitio... |
23,996 | lean_file_chunk | 79668114be002d0e4c1f905414d575ea7989cd38e9de04d29c5d320a75248c44 | 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, Floris van Doorn, Heather Macbeth
-/
module
public import Mathlib.Topology.FiberBundle.Trivialization
public import Mathlib.Topology.Order.LeftRightNhds
/-!
# F... |
20,336 | lean_file_chunk | a7996080aea346ba95004ad75e747dcfe3ee2718f67a234959102fc39f0c8a29 | lean_source_file | pkg_mathlib_source_file_chunks | map_source' p hp := by simpa using hp
map_target' p hp := by simpa using hp
left_inv' := by
rintro ⟨x, v⟩ hx
simp only [prodMk_mem_set_prod_eq, mem_inter_iff, and_true, mem_univ] at hx
dsimp only
rw [coordChange_comp, Z.coordChange_self]
exacts [hx.1, ⟨⟨hx.1, hx.2⟩, hx.1⟩]
right_inv' := by
... |
15,016 | lean_file_chunk | 96787c319b2258846a1becd04332374fba99569affc2afdbf3ce902cf31f1d51 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Nicolò Cavalleri. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nicolò Cavalleri, Sébastien Gouëzel, Heather Macbeth, Floris van Doorn
-/
module
public import Mathlib.Topology.FiberBundle.Basic
/-!
# Standard constructions on fiber bundles
Thi... |
23,942 | lean_file_chunk | 4d08b9b6086f4282dcf98685d75ccc3a197f04da646b994c431a729c60368e88 | 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.Data.Bundle
public import Mathlib.Data.Set.Image
public import Mathlib.Topology.CompactOpen
public import Mathlib.Topology.OpenPar... |
20,904 | lean_file_chunk | 55a3ee237fec37112b7e0ebca2cb15722ed26a57f56de330c988f47877e9289d | lean_source_file | pkg_mathlib_source_file_chunks | theorem preimageHomeomorph_symm_apply {s : Set B} (hb : s ⊆ e.baseSet) (p : s × F) :
(e.preimageHomeomorph hb).symm p =
⟨e.symm (p.1, p.2), ((preimageHomeomorph_symm_apply.aux e hb) p).2⟩ :=
rfl
/-- The source is homeomorphic to the product of the base set with the fiber. -/
def sourceHomeomorphBaseSetProd... |
14,545 | lean_file_chunk | 8b66843f111afa9f5d44aa9a94749bd8089071bfe72176de3220d8180657c02b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Jana Göken. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Artur Szafarczyk, Suraj Krishna M S, Jean-Baptiste Stiegler, Isabelle Dubois,
Tomáš Jakl, Lorenzo Zanichelli, Alina Yan, Emilie Uthaiwat, Jana Göken,
Filippo A. E. Nuccio
-/
module
public... |
2,653 | lean_file_chunk | 3bf00d578dbf6438d8c6c802dbc08ac25e27a628eba0c7d07325537937c3d817 | 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.Int.Interval
public import Mathlib.Data.Int.ConditionallyCompleteOrder
public import Mathlib.Topology.Instances.Dis... |
1,556 | lean_file_chunk | 2ebdf173e5afd52f3d277491d55c22c8ff553c0d2a33a0cb983c9b795ff6606a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
module
public import Mathlib.Data.Sign.Defs
public import Mathlib.Topology.Order.Basic
/-!
# Topology on `SignType`
This file gives `SignType` the discrete topology, a... |
20,049 | lean_file_chunk | 9b635273671b3bd81bc16fc15ca9d308dbf8442a727c63f79afdc0e3253b888f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash, Eric Wieser
-/
module
public import Mathlib.LinearAlgebra.Matrix.NonsingularInverse
public import Mathlib.Topology.Algebra.InfiniteSum.Basic
public import Mathlib.Topology.A... |
2,639 | lean_file_chunk | 86087be1d14f58a716b939d4fdf22da0644856b27b60422f84d4ccd8d1773743 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
module
public import Mathlib.Topology.Order.Basic
public import Mathlib.Order.SuccPred.LinearLocallyFinite
/-!
# Instances related to the discrete topology
We prove th... |
5,335 | lean_file_chunk | e5c61843480c4fe5d355f12184e8758badb74633750b5d207df1dae54e184b48 | 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.Algebra.Algebra.Rat
public import Mathlib.Algebra.Module.Rat
public import Mathlib.Data.NNRat.Order
public import Mathli... |
2,408 | lean_file_chunk | 4c6a97c3a23c302d74f046a37de4ba856f538c3f75fa81b58abcdbbf8f6a9a84 | 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.Algebra.Module.Equiv
public import Mathlib.Topology.Instances.Rat
public import Mathlib.Algebra.Module.Rat
/-!
# Continuous ... |
2,226 | lean_file_chunk | 2de0c0991b179c4b9a30da71e65c1704631beee4a8baff45c7d1295ec8c95091 | 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.Nat.Lattice
public import Mathlib.Topology.Instances.Int
/-!
# Topology on the natural numbers
The structure of a... |
4,991 | lean_file_chunk | 5935f1b86bf7d1e01d1918944b715951ff9bbb21f44d685ac22c42af01841c49 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Peter Nelson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Peter Nelson
-/
module
public import Mathlib.Data.ENat.Basic
public import Mathlib.Topology.Instances.Discrete
public import Mathlib.Order.Interval.Set.WithBotTop
public import Mathlib.... |
3,180 | lean_file_chunk | e493650984a94a3d0cd42da2f6ee922f3950bfe033a77e4f2e864dc23bc05176 | 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.Instances.Irrational
public import Mathlib.Topology.Instances.Rat
public import Mathlib.Topology.Compactification.OnePoint.Ba... |
1,220 | lean_file_chunk | 1d9cf6685d3eb22a87285b1f8a05f30940ff0b318d7fcbc98108b3c8df1e7655 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Miyahara Kō. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Miyahara Kō
-/
module
public import Mathlib.Topology.Instances.Nat
/-!
# Topology on the positive natural numbers
The structure of a metric space on `ℕ+` is introduced in this file, in... |
2,627 | lean_file_chunk | db6f6c1dee6ec31ce21828e6e37356792299f8fc94842b5f03afe1f79b8362f9 | 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.Algebra.Group.Subgroup.ZPowers.Lemmas
public import Mathlib.Algebra.Module.Submodule.Lattice
public import Mathlib.Topol... |
741 | lean_file_chunk | c72ad9c9e9b15e6a7b119de621b5bfab9e6ce92e8aae837841aafe8deb8e038c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
module
public import Mathlib.Logic.Small.Defs
public import Mathlib.Topology.Homeomorph.TransferInstance
/-!
# Topological space structure on `Shrink X`
-/
@[e... |
5,380 | lean_file_chunk | e213f2892f0d683c36d6a2afc3a73a9e83e0419362f86801aa146cdfc1d4ac25 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Xavier Roblot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Xavier Roblot
-/
module
public import Mathlib.Analysis.Complex.Basic
public import Mathlib.FieldTheory.IntermediateField.Basic
public import Mathlib.LinearAlgebra.Complex.FiniteDimensi... |
3,394 | lean_file_chunk | 4790637e0f097bb893da81659d44a0d75954dccf41103cd76fb56f6449fce2f5 | 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.Data.Rat.Encodable
public import Mathlib.NumberTheory.Real.Irrational
public import Mathlib.Topology.Separation.GDelta
public import M... |
523 | lean_file_chunk | 731ea07258771a0f2a24f4bdfefdab4e6d1f6a9b2d523e7fa598a714c3fb1584 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
module
public import Mathlib.Topology.Order
public import Mathlib.Data.ZMod.Defs
/-!
# Topology on `ZMod N`
We equip `ZMod N` with the discrete topology.
-/
@[exp... |
6,811 | lean_file_chunk | 3399a119f6d7da9bdd07ce2b22cb1d9ea18551203fb135e1e48979cf2553b9f9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
module
public import Mathlib.Algebra.TrivSqZeroExt.Basic
public import Mathlib.Topology.Algebra.InfiniteSum.Basic
public import Mathlib.Topology.Algebra.IsUniformGroup.Con... |
4,842 | lean_file_chunk | d39932f8f66dde82e52fc527bb57beaf45d53b0fadf9fd01fde3feec4bd9eb54 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.Topology.Convenient.GeneratedBy
/-!
# `X`-continuous maps
Given a family `X i` of topological spaces, we introduce a predicate
`ContinuousGenera... |
9,742 | lean_file_chunk | 2355379b15732dd1759a7a6a10d2dcfd440f51b509a051ef7e88ce4a2d85d106 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou, Dagur Asgeirsson, Ben Eltschig
-/
module
public import Mathlib.Topology.ContinuousMap.Basic
/-!
# The topology that is generated by a family of topological spaces
Let `X : ι →... |
2,876 | lean_file_chunk | b488a0cb1c61bb5b87699f6ac97a0e4c9cf6bd2804244ec9ed28f6222f1bc691 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Junyan Xu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Junyan Xu
-/
module
public import Mathlib.Algebra.Algebra.Defs
public import Mathlib.Topology.Covering.Quotient
public import Mathlib.Topology.Instances.AddCircle.Defs
/-!
# Covering maps... |
23,958 | lean_file_chunk | 9530d7530f250bedd756edaec34086e511789751bba89885dd5ae402c03dc4d5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
module
public import Mathlib.Topology.DiscreteSubset
public import Mathlib.Topology.FiberBundle.Basic
public import Mathlib.Topology.IsLocalHomeomorph
/-!
# Cover... |
5,771 | lean_file_chunk | f00445d432f96fbddb6c784a6327d1631129b80bf76adfd2b372ff5dcecc87f2 | lean_source_file | pkg_mathlib_source_file_chunks | rw [open_iff i Set.inter_subset_left]
convert ((open_iff i subset_rfl).mp open_V).inter open_W using 1
refine Set.ext fun e ↦ and_right_comm.trans (and_congr_right fun ⟨hV, hU⟩ ↦ ?_)
rw [Set.mem_preimage, dif_pos hV, inj i (inv_U i _) hU (f_inv i _)]
variable {s}
variable (f) in
theorem IsDiscrete.of_open... |
12,100 | lean_file_chunk | b63a6e6b7dc4292392c1b68a0e8cfbd8917820c1e7df4d757c3e07301f880644 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Junyan Xu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Junyan Xu
-/
module
public import Mathlib.GroupTheory.Coset.Defs
public import Mathlib.Topology.Algebra.ConstMulAction
public import Mathlib.Topology.Algebra.Group.Quotient
public import M... |
19,057 | lean_file_chunk | 3e921dc179b23f31d13a6267b4fd024f29818f0f852b891ba1a465fffd977c38 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Etienne Marion. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson, Etienne Marion
-/
module
public import Mathlib.Topology.Category.CompHaus.Basic
public import Mathlib.Topology.Compactification.OnePoint.Basic
/-!
# Compactly gener... |
236 | lean_file_chunk | 52678a592914c8a03c26882b6eb8e62c45036f6f42a269b8df4e90dbc948c89a | lean_source_file | pkg_mathlib_source_file_chunks | module -- shake: keep-all
import Mathlib.Analysis.Normed.Group.Basic
import Mathlib.Data.EReal.Inv
import Mathlib.Topology.Algebra.InfiniteSum.Order
import Mathlib.Topology.MetricSpace.Bounded
deprecated_module (since := "2025-12-18") |
4,528 | lean_file_chunk | b460c10e33f718141d137c1dde7e08709edece4747934a39eb0833070809a3f5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Floris van Doorn and Hannah Scholz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Hannah Scholz
-/
module
public import Mathlib.Topology.Coherent
public import Mathlib.Topology.Compactness.Compact
/-!
# Compactly coherent spac... |
2,382 | lean_file_chunk | 825f27a522ef95ba5db758644fc5925761706e37650c19e99121cac7037ddd7b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang, Dagur Asgeirsson
-/
module
public import Mathlib.Topology.Bases
public import Mathlib.Topology.Compactness.Compact
/-!
# Topological bases in compact sets and compact space... |
8,986 | lean_file_chunk | 8daa19010fdeb0af2efa399a6678d5b049752750ec22a16ccfd545ced2ec42f1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Ben Eltschig. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ben Eltschig
-/
module
public import Mathlib.Analysis.LocallyConvex.WithSeminorms
/-!
# Delta-generated topological spaces
This file defines delta-generated spaces, as topological spa... |
23,951 | lean_file_chunk | 0de33a0f65a1106f5b417d30e5170565400241e0797aa88e795930213abb397f | 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.Tendsto
public import Mathlib.Data.Set.Accumulate
public import Mathlib.Topology.Bornology... |
23,994 | lean_file_chunk | 258d9da42e138ea3ac016fce02aa7f94a46df19d2172921af18fbd79ec4231e5 | lean_source_file | pkg_mathlib_source_file_chunks | theorem Finset.isCompact_biUnion (s : Finset ι) {f : ι → Set X} (hf : ∀ i ∈ s, IsCompact (f i)) :
IsCompact (⋃ i ∈ s, f i) :=
s.finite_toSet.isCompact_biUnion hf
theorem isCompact_accumulate {K : ℕ → Set X} (hK : ∀ n, IsCompact (K n)) (n : ℕ) :
IsCompact (accumulate K n) :=
(finite_le_nat n).isCompact_biUn... |
12,783 | lean_file_chunk | cd04d816177a11348a46388cb0c91a6766fe81b093464d8007ec731decc0609c | lean_source_file | pkg_mathlib_source_file_chunks | obtain ⟨_, ⟨x, x_in : x ∈ s, rfl⟩, hx : ClusterPt (f x) (map f F)⟩ :=
hs ((map_mono F_le).trans_eq map_principal)
exact ⟨x, x_in, hf.mapClusterPt_iff.1 hx⟩
/-- If `f : X → Y` is an embedding, the image `f '' s` of a set `s` is compact
if and only if `s` is compact. -/
theorem Topology.IsEmbedding.isCompact_iff {... |
19,929 | lean_file_chunk | 4cddb98a6033ea1e5ee76a42abddf3ab674af45775bf9f683d88f7710d143a0c | 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.Bases
public import Mathlib.Topology.Compactness.LocallyCompact
public import Mathlib.Topology... |
513 | lean_file_chunk | ec1a1998c973c264cd1dc614ebe020c293185a9be77053d1efe4e5c135094cb4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Josha Dekker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Josha Dekker
-/
module -- shake: keep-all
public import Mathlib.Tactic.Linter.DeprecatedModule
public import Mathlib.Data.Finset.Attr
public import Mathlib.Tactic.Common
public import M... |
18,443 | lean_file_chunk | 226efee83a87f384ca3f4ff507295f1f84f26c4b8ddd384b97e7e12052f56b32 | 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: Reid Barton, Yury Kudryashov
-/
module
public import Mathlib.Data.Option.Basic
public import Mathlib.Topology.Separation.Regular
/-!
# Paracompact topological spaces
A topological ... |
23,955 | lean_file_chunk | 4f4e5f0be0a0ad6fe1fc67759872fb0b47bce840e54656820a4b2b8172ca6069 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Josha Dekker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Josha Dekker
-/
module
public import Mathlib.Topology.Bases
public import Mathlib.Order.Filter.CountableInter
public import Mathlib.Topology.Compactness.SigmaCompact
/-!
# Lindelöf set... |
13,419 | lean_file_chunk | 22597e747b256c7da3716e4082d1e0847fd40875b306d4b938fbec944a55fb8e | lean_source_file | pkg_mathlib_source_file_chunks | theorem LindelofSpace.elim_nhds_subcover [LindelofSpace X] (U : X → Set X) (hU : ∀ x, U x ∈ 𝓝 x) :
∃ t : Set X, t.Countable ∧ ⋃ x ∈ t, U x = univ := by
obtain ⟨t, tc, -, s⟩ := IsLindelof.elim_nhds_subcover isLindelof_univ U fun x _ => hU x
use t, tc
apply top_unique s
theorem lindelofSpace_of_countable_subf... |
11,294 | lean_file_chunk | 61cab54c3c7171b34bb9f3ceca5c7f9a522cdca6aa2fa351d1e0d568be2a58da | 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.Compactness.Compact
/-!
# Locally compact spaces
This file contains basic results about local... |
15,632 | lean_file_chunk | f114410ef2d089eb62ada209acc08df8512e6c7fd08213fb87b4ea5bd10f1e05 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Michał Świętek. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michał Świętek, Yongxi Lin
-/
module
public import Mathlib.Topology.Defs.Sequences
public import Mathlib.Topology.Separation.Basic
public import Mathlib.Topology.Compactness.Lindelof
... |
948 | lean_file_chunk | 6c607c92cf58158e22759aa842610df714080260882cd34b4d0522b5fff51797 | 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.Tactic.Peel
public import Mathlib.Topology.Compactness.Compact
public import Mathlib.Topology.NhdsKer
/-!
# Compactness of the neighb... |
7,283 | lean_file_chunk | 5aa804b51bb11678fcf3623b4b4e773651d449f4a7b5e4098756c0b4d4f13a28 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Peter Pfaffelhuber. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne, Peter Pfaffelhuber
-/
module
public import Mathlib.MeasureTheory.PiSystem
public import Mathlib.Topology.Separation.Hausdorff
/-!
# Compact systems
This file defin... |
2,088 | lean_file_chunk | 61342636244f543f4e6defdf3e7a0d2ccd86a851d01c04ba6eabee1a4560ecc1 | 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.Topology.LocallyFinite
public import Mathlib.Topology.Compactness.Compact
/-!
# Compact sets and compact spaces and locally finite fu... |
7,468 | lean_file_chunk | b6ccbb9c5b84caae8b4531a0d36a9ab018a51632fb554e7fce42ee0d844eb10d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Felix Weilacher. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Felix Weilacher
-/
module
public import Mathlib.Topology.LocallyClosed
public import Mathlib.MeasureTheory.MeasurableSpace.EventuallyMeasurable
public import Mathlib.MeasureTheory.Co... |
12,817 | lean_file_chunk | 4d1ed72004659700eaaa963d0871057ab1a3ff1541823318ef7fa719923d1645 | 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.Data.Fintype.Powerset
public import Mathlib.Topology.GDelta.Basic
public import Mathlib.Topology.Constructions
/-!
# Baire spaces... |
3,502 | lean_file_chunk | 9ad844adc5298ec1bc668a17d69df8aa19e86330f0490e41296a3b948cf2a5c9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Damien Thomine. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damien Thomine
-/
module
public import Mathlib.Topology.Sets.Compacts
/-!
# Second Baire theorem
In this file we prove that a locally compact regular topological space has Baire pro... |
5,321 | lean_file_chunk | 11c27151f0d31536c764a52e38b437ecb70126198c01a4f0662596b4e1ed5687 | 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, Yury Kudryashov
-/
module
public import Mathlib.Analysis.SpecificLimits.Basic
public import Mathlib.Tactic.Finiteness
public import Mathlib.Topology.Metrizable.C... |
14,494 | lean_file_chunk | 8312b3afe217744a9f463bc7e17c233974a58e39e995a37a8381bc51be3afcd9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Etienne Marion. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Etienne Marion
-/
module
public import Mathlib.Topology.MetricSpace.Gluing
public import Mathlib.Topology.Metrizable.Uniformity
/-!
# Completely (pseudo)metrizable spaces
A topologi... |
10,135 | lean_file_chunk | 2524c4217a96fa9fe443349f9689b4538337da44b5855f3c6f83d5f5c53dd8b5 | 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.Topology.UniformSpace.Pi
/-!
# Metrizable Spaces
In this file we define metrizable topological spaces, i.e., topological spaces for ... |
1,023 | lean_file_chunk | 036b582c0e583c8830fa93262e5fc9a26a16fdcace96926523dbc0ebb836a74c | 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.UniformSpace.CompactConvergence
public import Mathlib.Algebra.Order.Module.Field
public import Mathlib.Topology.MetricSpace.P... |
15,090 | lean_file_chunk | 766311838ec0488b79eaeaca073676adc85526bbe54d518eb9c5926304c88496 | 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.Data.Nat.Lattice
public import Mathlib.Data.NNReal.Basic
public import Mathlib.Topology.MetricSpace.Basic
public import Mathlib.Topolo... |
6,716 | lean_file_chunk | 6d9ae88b058e77c54dcf08d69acd77436e53def3091284f52df07c0a76f0a830 | 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.Analysis.SpecificLimits.Basic
public import Mathlib.Topology.UrysohnsLemma
public import Mathlib.Topology.Metrizable.Basic
public impo... |
774 | lean_file_chunk | db9b5dce411a6ccde16289a1b5cab80795247bb81a75024cab8747bfe34e28a9 | 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.Topology.MetricSpace.Basic
public import Mathlib.Topology.Metrizable.Basic
public import Mathlib.Topology.Order.Monotone... |
10,921 | lean_file_chunk | 73b6029c3861259c1821f490baca5d1fc91cb6ed7c8f6f9bd0335ca80bc95b31 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Johannes Hölzl
-/
module
public import Mathlib.Topology.Algebra.UniformMulAction
/-!
# Completion of topological groups:
This file endows the completion of a topolog... |
3,506 | lean_file_chunk | ec7390ca8733dd4ce624a34b096c0eb3549ff05465f4f521df4a8abb6b65b4e9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Nailin Guan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nailin Guan, Yi Song, Xuchun Li, Bryan Wang
-/
module
public import Mathlib.GroupTheory.Index
public import Mathlib.Topology.Algebra.Group.ClosedSubgroup
public import Mathlib.Topology.A... |
23,961 | lean_file_chunk | 9304049249338800549e98ca6a680dc301a0d4f669005110e3b76f1d05cb9eba | 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, Mitchell Lee
-/
module
public import Mathlib.Algebra.BigOperators.Finprod
public import Mathlib.Algebra.BigOperators.Pi
public import Mathlib.Algebra.G... |
21,725 | lean_file_chunk | f406bef75a252f0a296411a168651771831b8640dc14ee255102cb4d76b3748a | lean_source_file | pkg_mathlib_source_file_chunks | (hg.isCompact_insert_range_of_cocompact g_cont)
have K_mem_l : K ∈ l := eventually_map.mpr <| .of_forall fun ⟨x, y⟩ ↦
⟨mem_insert_of_mem _ (mem_range_self _), mem_insert_of_mem _ (mem_range_self _)⟩
have l_compact : Disjoint l (cocompact (M × M)) := by
rw [disjoint_cocompact_right]
exact ⟨K, K_mem_l, K_... |
4,353 | lean_file_chunk | e9a479bbb52330d5e5e0cf28ed9dbdff107a7157c0963f02e46a0f56967941bf | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
module
public import Mathlib.Analysis.SpecialFunctions.Complex.Circle
public import Mathlib.Topology.Algebra.Group.CompactOpen
/-!
# Pontryagin dual
This file de... |
1,786 | lean_file_chunk | 569246e63485f6513274b3dbb97226a91d21b3f6e529c92fee7f988005792c9f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 PFR contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: PFR contributors
-/
module
public import Mathlib.Algebra.Notation.Indicator
public import Mathlib.Topology.Piecewise
public import Mathlib.Topology.Clopen
/-!
# Continuity of indic... |
1,904 | lean_file_chunk | a000accd6fd73f2dfb74aab96a6fdf1391ab9c42d3fd2be4075b4496965bd175 | 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
-/
module
public import Mathlib.Topology.Algebra.FilterBasis
public import Mathlib.Topology.Algebra.IsUniformGroup.Defs
/-!
# Uniform properties of neighborhood bases ... |
18,685 | lean_file_chunk | d0a7f05f85a8a878c22b5657ea697ee53769573394fe5f8be0c03452c2aa0cb0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Nailin Guan, Yi Song, Xuchun Li
-/
module
public import Mathlib.RingTheory.Ideal.Defs
public import Mathlib.Topology.Algebra.Group.Quotient
public import Mathlib.Topol... |
21,553 | lean_file_chunk | aad59ec9368e7b415981b2004035306d3c626340fb7a8ec6b55001c2a773294b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Patrick Massot
-/
module
public import Mathlib.Algebra.Group.Submonoid.BigOperators
public import Mathlib.Algebra.GroupWithZero.Indicator
public import Mathlib.Alg... |
12,311 | lean_file_chunk | 5e7f457654b0b56173fc44b2638c6c4ed91a808f97848376bb75c426095a44e0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Johannes Hölzl
-/
module
public import Mathlib.Algebra.Algebra.Defs
public import Mathlib.Algebra.Module.Submodule.Lattice
public import Mathlib.Algebra.Ring.TransferI... |
3,048 | lean_file_chunk | 69a2665611fdc67bbe157360e1c6b443e7312b8e96e28990ea2bacec61053433 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
module
public import Mathlib.Topology.Algebra.Constructions
public import Mathlib.Topology.ContinuousMap.Defs
public import Mathlib.Algebra.Star.Basic
/-!
# Continuity of... |
23,978 | lean_file_chunk | 942d4d6e5735a21339d5d3049980507a6c82da2e9a55bbbc5797b61cad7ee669 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Alex Kontorovich, Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex Kontorovich, Heather Macbeth
-/
module
public import Mathlib.Algebra.Group.Pointwise.Set.Lattice
public import Mathlib.Algebra.GroupWithZero.Action.Pointwise.S... |
3,333 | lean_file_chunk | 22e75f1c18bd23a4ef53d4db56f5fecca2c44b56cd3f3a2c3b7daee54d259c99 | lean_source_file | pkg_mathlib_source_file_chunks | ⟨Quot.mk_surjective, continuous_quot_mk, isOpenMap_quotient_mk'_mul⟩
/-- The quotient by a discontinuous group action of a locally compact T₂ space is T₂. -/
@[to_additive /-- The quotient by a discontinuous group action of a locally compact T₂
space is T₂. -/]
instance (priority := 100) t2Space_of_properlyDiscontinuo... |
1,894 | lean_file_chunk | 5f0864b0f0e75c4c7ec31525158e9356c32eead17dc1249d40d9dbf2adcf19e6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
module
public import Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic
public import Mathlib.Topology.Algebra.ContinuousAffineMap
public import Mathlib.Topology.Alg... |
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