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 |
|---|---|---|---|---|---|
9,860 | lean_file_chunk | aeaf0137b5765d22088533b5d07a292ca366adc839976871b2b506780c7ea7ba | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, Calle Sönne, Dagur Asgeirsson
-/
module
public import Mathlib.CategoryTheory.FintypeCat
public import Mathlib.Topology.Category.CompHaus.Basic
public import Mathlib.Topo... |
2,115 | lean_file_chunk | f1631e274bfc1d0b81571bde5732db781bde0db5e8e6d526a76e69feb53ded40 | 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.Topology.Category.Profinite.Basic
public import Mathlib.Topology.Compactification.StoneCech
public import Mathlib.CategoryTheory.Preaddi... |
1,299 | lean_file_chunk | bd90239c06e157fc6fcfddce9e3d990ad5bfe3fd981bc6edb4c27c2025a3ba40 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz, Dagur Asgeirsson
-/
module
public import Mathlib.Topology.Category.Profinite.Basic
public import Mathlib.Topology.Category.CompHausLike.Limits
/-!
# Explicit limits and colim... |
8,056 | lean_file_chunk | e0bc3f792cf7f4cba095be7082107ce096414993e876984fbee5c7a366ac6c3a | 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.Category.Profinite.AsLimit
public import Mathlib.Topology.Category.Profinite.CofilteredLimit
public import Mathlib.Category... |
3,723 | lean_file_chunk | 37f549009ee973ee0c6dcd7d4fab0fe7a5c1b13adb42984f34ff881b47024b86 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Calle Sönne, Adam Topaz
-/
module
public import Mathlib.Topology.Category.Profinite.Basic
public import Mathlib.Topology.DiscreteQuotient
/-!
# Profinite sets as limits of finite sets.
... |
3,261 | lean_file_chunk | 47bf0499f71389d8b1c788ed48408150c5b605d98944e096cec18b8d7292201f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz, Dagur Asgeirsson
-/
module
public import Mathlib.Topology.Category.CompHaus.Limits
public import Mathlib.Topology.Category.CompHausLike.EffectiveEpi
/-!
# Effective epimorphi... |
8,076 | lean_file_chunk | 190a6fbaf7adc6eda868e36c68b29116b74b50135bbae6c206b206e107a05651 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz, Bhavik Mehta, Dagur Asgeirsson
-/
module
public import Mathlib.CategoryTheory.Monad.Limits
public import Mathlib.Topology.Compactification.StoneCech
public import Mathlib.Topo... |
2,300 | lean_file_chunk | fdd0435e20f77c980729a98c2e09848ea70f30dedf2710c85e487ef68f38c704 | 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.Topology.Category.CompHaus.Basic
public import Mathlib.Topology.Compactification.StoneCech
public import Mathlib.CategoryTheory.Preaddit... |
1,336 | lean_file_chunk | 4119c830bdcc358981129b54ad5b23989d468553625f99fd4543f36b61b46340 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz, Dagur Asgeirsson
-/
module
public import Mathlib.Topology.Category.CompHaus.Basic
public import Mathlib.Topology.Category.CompHausLike.Limits
/-!
# Explicit limits and colimi... |
969 | lean_file_chunk | 5d821df3ed26667db7292c9316d66f6f5bb0bcb165ead718c5bc218c62280ea4 | 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.Category.Frm
public import Mathlib.Topology.Category.CompHaus.Basic
public import Mathlib.Topology.Sets.Opens
/-! The forgetful funct... |
3,386 | lean_file_chunk | 047b42028ab6d4a74588ab89274daf30a29956b0c6c1075ce345eb54f27b43df | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Jon Eugster. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson, Boris Bolvig Kjær, Jon Eugster, Sina Hazratpour, Nima Rasekh
-/
module
public import Mathlib.CategoryTheory.Sites.Coherent.ReflectsPreregular
public import Mathlib.Topo... |
10,615 | lean_file_chunk | 37cafb9d6b1ed098538d6acf02900158965906ef7eaf8c4c0676753e8577a495 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz, Dagur Asgeirsson
-/
module
public import Mathlib.Topology.ExtremallyDisconnected
public import Mathlib.Topology.Category.CompHaus.Projective
public import Mathlib.Topology.Cat... |
2,478 | lean_file_chunk | e4310727b7b28495a55b684a629cbb386d2fe10b9eba0dcb0365f85e2be20cd9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz, Dagur Asgeirsson, Filippo A. E. Nuccio, Riccardo Brasca
-/
module
public import Mathlib.Topology.Category.CompHausLike.Limits
public import Mathlib.Topology.Category.Stonean.B... |
2,334 | lean_file_chunk | fa07385f5099719a3b9bab520e3f914f69f0c6248917e6d1ebbd9aea2307c42d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 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.Category.Stonean.Basic
public import Mathlib.Topology.Category.TopCat.Adjunctions
public import Mathlib.Topology.Compactifi... |
12,822 | lean_file_chunk | adbba4764b78e04c93a8685c15d39206d9c769fd1de09e1162e84a2246689308 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Kim Morrison, Mario Carneiro, Andrew Yang
-/
module
public import Mathlib.Topology.Category.TopCat.EpiMono
public import Mathlib.Topology.Category.TopCat.Limits.Basic
pu... |
5,418 | lean_file_chunk | 543c16a1a3759dc71cb60e4ae64cee3b61cb5b4d88c7040e0e865fccc45cffc5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller
-/
module
public import Mathlib.CategoryTheory.Filtered.Basic
public import Mathlib.Topology.Category.TopCat.Limits.Basic
/-!
# Topological Kőnig's lemma
A topological vers... |
12,387 | lean_file_chunk | 7298a3989a7b0cde9361404369d72c69d60a1cc0c7c6066b0308bd550d1bb1f3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Kim Morrison, Mario Carneiro, Andrew Yang
-/
module
public import Mathlib.Topology.Category.TopCat.Adjunctions
public import Mathlib.CategoryTheory.Limits.Types.Limits
p... |
3,667 | lean_file_chunk | c7e61c4bd63d82b0f40ca8552566f389c10072ebaf1e2c01be61844b9e480993 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Kim Morrison, Mario Carneiro, Andrew Yang
-/
module
public import Mathlib.Topology.Category.TopCat.Limits.Basic
public import Mathlib.CategoryTheory.Filtered.Basic
/-!
... |
16,806 | lean_file_chunk | d7bd3d041384d0dff58dfc92cf9d4f779e3cec7c40df8649210bc8d18f0690ff | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Kim Morrison, Mario Carneiro, Andrew Yang
-/
module
public import Mathlib.Topology.Category.TopCat.Limits.Products
/-!
# Pullbacks and pushouts in the category of topol... |
23,991 | lean_file_chunk | c01823a3b08a125f38eaf7e1b584a452285dbec5a335f71fa54e54b53f32737c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
module
public import Mathlib.Algebra.Homology.ShortComplex.ModuleCat
public import Mathlib.Topology.Category.Profinite.Nobeling.Basic
/-!
# The successor case i... |
699 | lean_file_chunk | 59bdfd97e1b54d1166ae9e2daf158accb6f8fa40b8d0b10c1a1a130c11c231da | lean_source_file | pkg_mathlib_source_file_chunks | dsimp [MaxToGood] at h
rw [max_eq_o_cons_tail C hsC ho m, max_eq_o_cons_tail C hsC ho n, h]
include hC in
theorem linearIndependent_comp_of_eval
(h₁ : ⊤ ≤ Submodule.span ℤ (Set.range (eval (π C (ord I · < o))))) :
LinearIndependent ℤ (eval (C' C ho)) →
LinearIndependent ℤ (ModuleCat.ofHom (Linear_CC' C h... |
23,954 | lean_file_chunk | 563f7444c5cc5e663d840bf8149e6e79b028f96ac6806080e39b845aedee0cf1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
module
public import Mathlib.LinearAlgebra.LinearIndependent.Defs
public import Mathlib.SetTheory.Ordinal.Basic
public import Mathlib.Topology.Category.Profinite... |
317 | lean_file_chunk | 8aa72b55c5c87284af5580e0fdf65c5ad072755421fa983a0e5ed5251b3d7a64 | lean_source_file | pkg_mathlib_source_file_chunks | (hl : l.isGood (π C (ord I · < o₁))) : l.isGood (π C (ord I · < o₂)) := by
intro hl'
apply hl
rwa [eval_πs_image' C h (prop_of_isGood C _ hl), ← eval_πs' C h (prop_of_isGood C _ hl),
Submodule.apply_mem_span_image_iff_mem_span (injective_πs' C h)] at hl'
end Products
end Maps
end Profinite.NobelingProof |
9,977 | lean_file_chunk | e12f5e4d475bfa53108fec8bcbc6dd382ebffa6ac289fdfc333e4845370a0c30 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
module
public import Mathlib.Data.Finset.Sort
public import Mathlib.Tactic.NoncommRing
public import Mathlib.Topology.Category.Profinite.CofilteredLimit
public i... |
9,859 | lean_file_chunk | 1d33861a456bad4664ef1ccfac3cfaca2eb601f655e8f82909cb69ec90c3c29a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
module
public import Mathlib.LinearAlgebra.LinearIndependent.Basic
public import Mathlib.Topology.Category.Profinite.Nobeling.Basic
/-!
# The zero and limit cas... |
5,488 | lean_file_chunk | 2b5f35ce3294bbd8fc3c7e51883c1f5d448421cbd484df7cc3de6e6fcdc5ec48 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
module
public import Mathlib.Algebra.Category.ModuleCat.Free
public import Mathlib.Topology.Category.Profinite.Nobeling.Span
public import Mathlib.Topology.Categ... |
23,911 | lean_file_chunk | ec1091d7a51c17a9c6aaf2c093ac82ece6fa281ab30224009bf9b3e3595b2a7f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Mario Carneiro, Yury Kudryashov, Heather Macbeth
-/
module
public import Mathlib.Algebra.Module.MinimalAxioms
public import Mathlib.Analysis.Normed.Order.Lattice... |
465 | lean_file_chunk | 57e2e1dc0e3789906f707af10df6baba8e8c2eefa7e4d915cf807a2cc368a1ec | lean_source_file | pkg_mathlib_source_file_chunks | simp only [ContinuousMap.toFun_eq_coe, coe_toContinuousMap, coe_zero, Pi.zero_apply, coe_add,
const_apply, Pi.add_apply]
linarith [(abs_le.mp (norm_coe_le_norm f x)).1]
lemma norm_sub_nonneg (f : α →ᵇ ℝ) :
0 ≤ const _ ‖f‖ - f := by
intro x
simp only [ContinuousMap.toFun_eq_coe, coe_toContinuousMap, coe_z... |
3,489 | lean_file_chunk | 20a491ec348f32e2de27ae841b495943854d4b4dc803af0ee5c43594d6cce30e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Mario Carneiro, Yury Kudryashov, Heather Macbeth
-/
module
public import Mathlib.Analysis.CStarAlgebra.Basic
public import Mathlib.Topology.ContinuousMap.Bounded... |
6,316 | lean_file_chunk | 0f5536a8ed16e05af5d8d963bcaf7bb83828c9ab94445bb78a8e95966eba0a1a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Mario Carneiro, Yury Kudryashov, Heather Macbeth
-/
module
public import Mathlib.Topology.ContinuousMap.Bounded.Basic
public import Mathlib.Topology.MetricSpace.... |
23,988 | lean_file_chunk | 880f676ffe508c140ba7fe2c8259001ffa33adc5f8819b0ccf3e4e54e6084940 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Mario Carneiro, Yury Kudryashov, Heather Macbeth
-/
module
public import Mathlib.Topology.Algebra.Indicator
public import Mathlib.Topology.Bornology.BoundedOpera... |
8,398 | lean_file_chunk | 865bf9b995876ba920a636fb5a47b6999ee4d2cead33866a18fb7c08d9b0a047 | lean_source_file | pkg_mathlib_source_file_chunks | @[to_additive (attr := simp)]
lemma coe_prod {ι : Type*} (s : Finset ι) [CommMonoid R] [BoundedMul R] [ContinuousMul R]
(f : ι → α →ᵇ R) :
⇑(∏ i ∈ s, f i) = ∏ i ∈ s, ⇑(f i) := map_prod coeFnMonoidHom f s
@[to_additive]
lemma prod_apply {ι : Type*} (s : Finset ι) [CommMonoid R] [BoundedMul R] [ContinuousMul R]
... |
1,659 | lean_file_chunk | 3263a6ada6a1a89aeeabd899731d9faf852c27472bf89d2efcafe0812c36e6b0 | 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.AlgebraicTopology.SimplicialSet.Homotopy
public import Mathlib.AlgebraicTopology.SimplicialSet.TopAdj
public import Mathlib.Topology.Homotopy.TopC... |
1,219 | lean_file_chunk | a170b30d8ec3fc8443f75f76cc2b288c4e6535b786f320ac08799bee913fccf0 | 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.Category.TopCat.Monoidal
public import Mathlib.Topology.Homotopy.Basic
/-!
# Homotopies between morphisms in `TopCat`
In this file, we ... |
23,990 | lean_file_chunk | f0549f0a51623dc9ff15e566c2c21092ef00443bb549db6e90952d4309a0043c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Yourong Zang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yourong Zang, Yury Kudryashov
-/
module
public import Mathlib.Data.Fintype.Option
public import Mathlib.Topology.Homeomorph.Lemmas
public import Mathlib.Topology.Sets.Opens
/-!
# The o... |
2,138 | lean_file_chunk | da69e759028241d15a5f1e82ad1f9423e5d7b139ff96ae4681b9bbace2b47ec0 | lean_source_file | pkg_mathlib_source_file_chunks | induction p using OnePoint.rec with
| infty => simp
| coe p =>
have hp : f p ≠ y := by simpa [hy] using mem_range_self (f := f) p
simpa [hp] using hf.injective (mem_range_self p).choose_spec
right_inv := fun q ↦ by
rcases eq_or_ne q y with rfl | hq
· simp
... |
8,232 | lean_file_chunk | 05b56e625b5696278101d36c9701591b87e6b635b6c3308d68c5557abfd33984 | 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, Oliver Nash
-/
module
public import Mathlib.Algebra.QuadraticDiscriminant
public import Mathlib.Data.Matrix.Action
public import Mathlib.LinearAlgebra.Matrix.G... |
1,920 | lean_file_chunk | 00998033d2e2d1b183214347a837be581fe2227f6827f2f8650e8fad963ee750 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Bjørn Kjos-Hanssen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bjørn Kjos-Hanssen, Oliver Nash
-/
module
public import Mathlib.Topology.Compactification.OnePoint.Basic
public import Mathlib.Geometry.Manifold.Instances.Sphere
/-!
# One-point... |
3,406 | lean_file_chunk | 81a44e83cacd97728205c89a11afd49c8fb4a917395cf3a3cf869653816bb3e6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 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.Compact
public import Mathlib.Topology.MetricSpace.Bounded
public import Mathlib.Topology.Order.IntermediateValue
p... |
1,692 | lean_file_chunk | 72ea62818d2bfcba9612a9a2b45e4c2e4f24c912055ba3202ae2f2611f983780 | 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.Rat.Encodable
public import Mathlib.Topology.MetricSpace.Isometry
public import Mathlib.Topology.MetricSpace.Proper... |
814 | lean_file_chunk | 5f239e3a02250a64fb791d42a8aa03e876e0b98641844b92ab4388eb7cbd8899 | 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.ContinuousMap.Compact
public import Mathlib.Topology.MetricSpace.Ultra.Basic
/-!
# Ultrametric structure on continuous maps
-/... |
960 | lean_file_chunk | f51b13f5e650837a41c44cc7b6fd1c6800601adedc3643accef55d9233c11a87 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-/
module
public import Mathlib.Topology.MetricSpace.Pseudo.Pi
public import Mathlib.Topology.MetricSpace.Ultra.Basic
/-!
# Ultrametric distances on pi types
This f... |
6,461 | lean_file_chunk | 64862cfb030e86108d2611a81bd09f9357d5e1ea10f3edf475bd668b5bbfd5b3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-/
module
public import Mathlib.Topology.MetricSpace.Pseudo.Lemmas
public import Mathlib.Topology.Clopen
/-!
## Ultrametric spaces
This file defines ultrametric spa... |
1,118 | lean_file_chunk | a7c1c3fbbb957d25a4f2fc730b165febd43146d4847865915171a814a19bd1cd | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky, David Loeffler
-/
module
public import Mathlib.Topology.Connected.TotallyDisconnected
public import Mathlib.Topology.MetricSpace.Defs
public import Mathlib.Topology.... |
5,574 | lean_file_chunk | f1b60f3e096c32f9ad67a6e15b6a353e358d03a45f6ed3f26e01723d35bff934 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2015 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Robert Y. Lewis, Johannes Hölzl, Mario Carneiro, Sébastien Gouëzel
-/
module
public import Mathlib.Topology.MetricSpace.Pseudo.Constructions
public import Mathlib.Topolo... |
8,277 | lean_file_chunk | 3e8d878cb22b2a11a0fa9dc969593662a6c4ef9de8e80c46fa8bbdea460c8dcc | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2015 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Robert Y. Lewis, Johannes Hölzl, Mario Carneiro, Sébastien Gouëzel
-/
module
public import Mathlib.Data.ENNReal.Lemmas
public import Mathlib.Topology.Bornology.Construct... |
13,050 | lean_file_chunk | dedb3eca2d02772eb74499895ae8e6a55bb30c1c5bbc4294e1d9d8ee9a7736bc | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2015 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Robert Y. Lewis, Johannes Hölzl, Mario Carneiro, Sébastien Gouëzel
-/
module
public import Mathlib.Data.ENNReal.Real
public import Mathlib.Tactic.Bound.Attribute
public ... |
10,059 | lean_file_chunk | cacdfc36c1f14dc5a76c34627fb5cfecd2e05f9b02c3190ba1880bb6a86d147d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2015 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Robert Y. Lewis, Johannes Hölzl, Mario Carneiro, Sébastien Gouëzel
-/
module
public import Mathlib.Topology.Bornology.Constructions
public import Mathlib.Topology.Metric... |
23,970 | lean_file_chunk | 3d70e6e14d7e0cfddf328290b46287d93f2359ea633950fcd11d71025270d9a7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2015 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Robert Y. Lewis, Johannes Hölzl, Mario Carneiro, Sébastien Gouëzel
-/
module
public import Mathlib.Data.ENNReal.Real
public import Mathlib.Tactic.Bound.Attribute
public ... |
23,961 | lean_file_chunk | 4600668153ee847e16c835e61bdc7de46bb9701f6e956603b87eed3035df9aeb | lean_source_file | pkg_mathlib_source_file_chunks | theorem ball_half_subset (y) (h : y ∈ ball x (ε / 2)) : ball y (ε / 2) ⊆ ball x ε :=
ball_subset <| by rw [sub_self_div_two]; exact le_of_lt h
theorem exists_ball_subset_ball (h : y ∈ ball x ε) : ∃ ε' > 0, ball y ε' ⊆ ball x ε :=
⟨_, sub_pos.2 h, ball_subset <| by rw [sub_sub_self]⟩
/-- If a property holds for al... |
7,757 | lean_file_chunk | feea316f1cb85a22cbcc6b58deee61f939fbebfd6dd445a6f576a54a6d8eb217 | lean_source_file | pkg_mathlib_source_file_chunks | /-- Build a new pseudometric space from an old one where the bundled bornology structure is provably
(but typically non-definitionaly) equal to some given bornology structure.
See Note [forgetful inheritance].
See Note [reducible non-instances].
-/
abbrev PseudoMetricSpace.replaceBornology {α} [B : Bornology α] (m : Ps... |
1,842 | lean_file_chunk | e8a31406474fe4e263fb42ca98ed0af74ab0db215faa7836488e3d1f36dde06f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2015 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Robert Y. Lewis, Johannes Hölzl, Mario Carneiro, Sébastien Gouëzel
-/
module
public import Mathlib.Algebra.Order.Group.Pointwise.Interval
public import Mathlib.Topology.... |
3,430 | lean_file_chunk | 01a1bb4359ad5ec6583a679f427947ad5507a220619eb57bd9a099b31db96066 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-/
module
public import Mathlib.Topology.UniformSpace.Completion
public import Mathlib.Topology.UniformSpace.Ultra.Basic
public import Mathlib.Topology.UniformSpace.U... |
8,669 | lean_file_chunk | 74e505933ebf43f19770a95d1b362056867e2cab909664706697be74cee83459 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-/
module
public import Mathlib.Topology.UniformSpace.Defs
public import Mathlib.Topology.Bases
/-!
# Ultrametric (nonarchimedean) uniform spaces
Ultrametric (nonar... |
3,729 | lean_file_chunk | 4709dcebda07204d2691d27594c0085f40adecbdf49cc04b1ca998b43479c0b8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-/
module
public import Mathlib.Topology.UniformSpace.DiscreteUniformity
public import Mathlib.Topology.UniformSpace.Pi
public import Mathlib.Topology.UniformSpace.Ul... |
11,468 | lean_file_chunk | 10c824b028a461482c76578207091ea81fedeec7d71706fb69a13f02c5c05bb2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
module
public import Mathlib.Data.NNReal.Basic
public import Mathlib.Topology.Algebra.InfiniteSum.Order
public import Mathlib.Topology.Algebra.InfiniteSum.Ring
publi... |
9,018 | lean_file_chunk | 88441f83f9a2f488188917d3938edcc35caa1c1ec35c2d824c910a6de6c03e0a | 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.Field.Periodic
public import Mathlib.Algebra.Field.Subfield.Basic
public import Mathlib.Topology.Algebra.Order.A... |
23,961 | lean_file_chunk | 954fd757604ea75b43bd6eec54e906da7b8271e789c8c1fbde7feefad672a643 | 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
-/
module
public import Mathlib.Algebra.BigOperators.Intervals
public import Mathlib.Data.ENNReal.BigOperators
public import Mathlib.Topology.Order.LiminfLimsup
public ... |
19,187 | lean_file_chunk | 2bf9e48453b2d792effecb1dc948062a377610b16aac132c4af74e0606aae0af | lean_source_file | pkg_mathlib_source_file_chunks | · obtain ⟨R, hR⟩ := exists_frequently_lt_of_liminf_ne_top' hf
obtain ⟨q, hq⟩ := exists_rat_lt R
refine ⟨q - 1, q, (sub_lt_self_iff _).2 zero_lt_one, ?_, ?_⟩
· simp only [IsBoundedUnder, IsBounded, eventually_map, not_exists] at hbdd
refine fun hcon => hbdd ↑(q - 1) ?_
filter_upwards [hcon] with ... |
23,961 | lean_file_chunk | c093c653c4fe76e3cb9681ae929eeab88f21c6f9110a7506306738233ba6dcff | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
module
public import Mathlib.Algebra.Order.ToIntervalMod
public import Mathlib.Algebra.Ring.AddAut
public import Mathlib.Data.Nat.Totient
public import Mathlib.GroupTheory... |
10,746 | lean_file_chunk | 7ff7521f6daf0a67c260dd0771a8ebebc57488008e6d6b9d65fd848c12cb3033 | lean_source_file | pkg_mathlib_source_file_chunks | · rwa [← addOrderOf_pos_iff, addOrderOf_period_div hn]
theorem addOrderOf_div_of_gcd_eq_one {m n : ℕ} (hn : 0 < n) (h : m.gcd n = 1) :
addOrderOf (↑(↑m / ↑n * p) : AddCircle p) = n := by
convert gcd_mul_addOrderOf_div_eq p m hn
rw [h, one_mul]
theorem addOrderOf_div_of_gcd_eq_one' {m : ℤ} {n : ℕ} (hn : 0 < n)... |
3,816 | lean_file_chunk | 6af5f69a386959ee11f848ab37111f3c1d07ab255e0ea7c2f78589b521998346 | 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.NumberTheory.Real.Irrational
public import Mathlib.Topology.Instances.AddCircle.Defs
public import Mathlib.Topology.Algebra.Order.Arch... |
2,927 | lean_file_chunk | 170325cf9286ab275dc3bae0d835e277f380b78833c22a0660e9f64033a901cf | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
module
public import Mathlib.Topology.Connected.PathConnected
public import Mathlib.Topology.Instances.AddCircle.Defs
public import Mathlib.Topology.Instances.ZMultiples
... |
23,998 | lean_file_chunk | 22ab0df36f190a21af3cf4e04d3baba8c3fbfaace7bd2441840a34bbbd5a92c8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 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.EReal.Inv
public import Mathlib.Topology.Semicontinuity.Basic
/-!
# Topological structure on `EReal`
We prove basic propert... |
2,630 | lean_file_chunk | 4dfba1af3ccd466fa7b640a4908ed66ec364484200326cf020d81fc70e39031d | lean_source_file | pkg_mathlib_source_file_chunks | · exact neg_neg a ▸ continuousAt_mul_symm2 (continuousAt_mul_top_pos (neg_pos.2 a_neg))
· exact continuousAt_mul_top_pos a_pos
/-- The multiplication on `EReal` is continuous except at indeterminacies
(i.e. whenever one value is zero and the other infinite). -/
theorem continuousAt_mul {p : EReal × EReal} (h₁ : p.1 ... |
1,510 | lean_file_chunk | bbe76d7f019306c4445fe235bda405be18366b6f39e999e2feb0356fbd4b3423 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Yoh Tanimoto. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yoh Tanimoto
-/
module
public import Mathlib.Algebra.Order.Group.Indicator
public import Mathlib.Topology.Algebra.Support
/-!
# The topological support of sup and inf of functions
In ... |
808 | lean_file_chunk | d7a3bb325822e9a731d63b9a8d7f458849f26f77becdf006bac2517ee5b3a3ba | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Algebra.Order.Nonneg.Module
public import Mathlib.Topology.Algebra.ConstMulAction
public import Mathlib.Topology.Algebra.MulAction
/-!
# Co... |
5,614 | lean_file_chunk | f5690ee1702739267dff723f93e97ebb34ac5b11e493fc12467de848a2c8de9e | 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.Order.Group.Basic
public import Mathlib.Topology.Algebra.Group.Defs
public import Mathlib.Topology.Order.LeftRightNhds
/-!
# ... |
12,933 | lean_file_chunk | 96c57c33544498ed9fdaa6daf198e422279007cb9ce5d9d85dc352ac71a35cad | 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.Algebra.Order.Group.DenselyOrdered
public import Mathlib.Data.Real.Archimedean
public imp... |
4,867 | lean_file_chunk | 7dbf98e85bd8f00804d455d88a359dd09d0f814dd910c70a37b3fb9525318480 | 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.GroupTheory.Archimedean
public import Mathlib.Topology.Algebra.Order.Group
public import Mathlib.Algebra.Group.Subgroup.ZPowers.Basic
... |
3,985 | lean_file_chunk | e4a96fec767b50dbbc6638cead71b8608b2a06a74a574bbb98447776ad528588 | 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.Algebra.Order.UpperLower
public import Mathlib.Topology.Algebra.Group.Pointwise
/-!
# Topological facts about upper/lower/order-connected s... |
3,102 | lean_file_chunk | bdff5dc7cde4e0dc63bf428e00175748b68b23de33bfe87a0c36230538b25f2d | 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.GroupTheory.ArchimedeanDensely
public import Mathlib.GroupTheory.SpecificGroups.Cyclic
public import Mathlib.Topology.Algebra.IsUniformG... |
10,250 | lean_file_chunk | e3bfbc959bdb6364f76bc9eab877cd3c4380027646fea979732ff2b8a9b578f1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker
-/
module
public import Mathlib.Algebra.Order.Floor.Ring
public import Mathlib.Order.Filter.AtTopBot.Floor
public import Mathlib.Topology.Algebra.Order.Group
/-!
#... |
15,215 | lean_file_chunk | a01720b09835a84ef8cedd7cd2dd96cb89e8665f6ed70898166a13c2cf3e1844 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Benjamin Davidson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Benjamin Davidson, Devon Tuma, Eric Rodriguez, Oliver Nash
-/
module
public import Mathlib.Algebra.Order.Group.Pointwise.Interval
public import Mathlib.Order.Filter.AtTopBot.Field
... |
1,022 | lean_file_chunk | 981e95e1ba621735ffb24d26a4cf2018d4b3a86fe1a850c4f91b69250474b32f | 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
-/
module
public import Mathlib.Topology.Algebra.Monoid
public import Mathlib.LinearAlgebra.Finsupp.Pi
/-!
# Continuity of the functoriality of `X → M` when `X` is finite
-/
p... |
7,225 | lean_file_chunk | f36a0e534e02ede128c3af43c28f2f791f80ebe4a704f5fb050baf205fa04464 | 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
-/
module
public import Mathlib.Topology.Constructions.SumProd
public import Mathlib.Algebra.Group.Basic
/-!
# Topological monoids - definitions
In this file we defin... |
762 | lean_file_chunk | 8357df5533fc737cd31b8cf2287cf956f4ae6501025f6560a647355cb0ed643c | 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.Algebra.Group.AddChar
public import Mathlib.Topology.DenseEmbedding
/-!
# Additive characters of topological monoids
-/
public section... |
21,112 | lean_file_chunk | ee88810258e477d7ccb6f7e8984f747099210733ecc6e3b50cd997817d2c5252 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker
-/
module
public import Mathlib.Algebra.Ring.Pi
public import Mathlib.Algebra.Ring.Subring.Defs
public import Mathlib.GroupTheory.GroupAction.SubMulAction
public im... |
3,970 | lean_file_chunk | b5b1bc87e5c00d9554f6fdba79673287c306777097de1efeeee3b4cd15e4a012 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Salvatore Mercuri. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Salvatore Mercuri
-/
module
public import Mathlib.Topology.Algebra.RestrictedProduct.Basic
public import Mathlib.Algebra.Group.Submonoid.Units
public import Mathlib.Algebra.Group.P... |
23,982 | lean_file_chunk | 364ac24d0d027e33d019d0a970ab8c6a7981f3ee9904fdb8352cb58aa7789dcf | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker
-/
module
public import Mathlib.Topology.Algebra.Group.Pointwise
public import Mathlib.Topology.Algebra.RestrictedProduct.Basic
public import Mathlib.Topology.Algeb... |
6,264 | lean_file_chunk | a68cb231a72f5ec31dd0e91bc297765f13e3c4a6126939d972737f6710ddffed | lean_source_file | pkg_mathlib_source_file_chunks | variable {S : ι → Type*} -- subobject type
variable [Π i, SetLike (S i) (R i)]
variable {B : Π i, S i}
variable {T : Set ι} {𝓕 : Filter ι}
variable [Π i, TopologicalSpace (R i)]
section general
@[to_additive]
instance [Π i, Inv (R i)] [∀ i, InvMemClass (S i) (R i)] [∀ i, ContinuousInv (R i)] :
ContinuousInv (Πʳ ... |
9,288 | lean_file_chunk | 8b8031de71c794ca98333a723c37be710f86f32688dc176e5186ee54609296f0 | 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, Nailin Guan
-/
module
public import Mathlib.Topology.Algebra.ContinuousMonoidHom
public import Mathlib.Topology.Algebra.Equicontinuity
public import Mathlib.Topology... |
6,326 | lean_file_chunk | 5f7726ec773f4ea8b49677b590d55f4508b5cc83b602a19598f0b3ea57b8aa8f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 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.Baire.Lemmas
public import Mathlib.Topology.Algebra.Group.Pointwise
/-! # Open mapping theorem for morphisms of topologi... |
6,925 | lean_file_chunk | deeb0cd36dba12cbd34876a34cd1685fd21b7e2c6791f282cb0caea51e277fb8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
module
public import Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.FinTwo
public import Mathlib.Topology.Algebra.Algebra
public import Mathlib.Topology.Algebra.Gr... |
1,081 | lean_file_chunk | fe24a89d3bfcd700db8ebec44299e54ae837b3c38d928d3e56518b455ba9ac6e | 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.Algebra.Group.Pointwise
public import Mathlib.Topology.Sets.Compacts
/-!
# Additional results ... |
3,871 | lean_file_chunk | 45b09e0bed37b89051467d0579cdb26479995ff335e0beac70c96d95b24dae29 | 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.Algebra.AddTorsor.Basic
public import Mathlib.Topology.Algebra.Monoid
public import Mathlib.Topology.Algebra.Group.Defs
/-!
# Topological... |
5,304 | lean_file_chunk | 85ecd91b0de5614a29c77b5e26775bf80f91d423b7dd8707e38f302f4bbfa915 | 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.Algebra.Group.Subgroup.ZPowers.Basic
public import Mathlib.Order.Filter.AtTopBot.Group
public import Mathlib.Topology.Algebra.Group.Ba... |
14,890 | lean_file_chunk | 3fdb8b64e8dff7112aa29200a6da03e9cef78097f5508ad49d78c59edc2045ff | 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.Algebra.Group.Basic
public import Mathlib.Topology.Maps.Proper.Basic
/-!
# Pointwise operation... |
2,246 | lean_file_chunk | 65afe98c7d769848dd6999c25a0299270061981f092c2bb55469370566c71752 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
module
public import Mathlib.Algebra.Exact
public import Mathlib.Topology.Algebra.Group.Quotient
/-!
# Short exact sequences of topological groups
In this file, ... |
23,991 | lean_file_chunk | f51cad7a2ccbc633fd3843811e45b63891f376799c66fa41f6c9ea69d69570d0 | 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.Algebra.Group.Subgroup.Pointwise
public import Mathlib.Algebra.Group.Submonoid.Units
public import Mathl... |
23,998 | lean_file_chunk | b2f32636dc5701b92cf6b6dbd615c8b5867a8d2bd2962aeb40161e3a8171ef43 | lean_source_file | pkg_mathlib_source_file_chunks | itself a subgroup. -/
@[to_additive
/-- The (topological-space) closure of an additive subgroup of an additive topological group is
itself an additive subgroup. -/]
def Subgroup.topologicalClosure (s : Subgroup G) : Subgroup G :=
{ s.toSubmonoid.topologicalClosure with
carrier := _root_.closure (s : Set G)
... |
9,517 | lean_file_chunk | aa6023ddc7e4be336130eb7e345ef8d899cbdfbdf74b118a236204130e14c7dd | lean_source_file | pkg_mathlib_source_file_chunks | open MulOpposite
/-- Given a compact set `K` inside an open set `U`, there is an open neighborhood `V` of `1`
such that `V * K ⊆ U`. -/
@[to_additive
/-- Given a compact set `K` inside an open set `U`, there is an open neighborhood `V` of
`0` such that `V + K ⊆ U`. -/]
theorem compact_open_separated_mul_left {K ... |
5,742 | lean_file_chunk | e4e66e8e7a17a787bd3a4a33e680cc47e4407b1e2842f5fd1a754e7f5d633408 | 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, Yury Kudryashov
-/
module
public import Mathlib.GroupTheory.GroupAction.Quotient
public import Mathlib.GroupTheory.QuotientGroup.Defs
p... |
7,273 | lean_file_chunk | 7b9bcdbc13afac5fcbbb7f12430cb0b39bad7d1d8320c20093f8c720617a285a | 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.Algebra.Group.Basic
/-!
### Lattice of group topologies
We define a type class `GroupTopology... |
6,576 | lean_file_chunk | 15a6e42ee4bfa4f18e5c83a60f0eaaa4024dd2eea602affd0fa500da174fae55 | 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.Algebra.Monoid.Defs
/-!
# Definitions about topological groups
In this file we define mixin c... |
3,265 | lean_file_chunk | 38c5a712932807a8c7cb69df069dee1f78b6d26c442d83e3b33d4689f7938c96 | 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
-/
module
public import Mathlib.Algebra.Group.Subgroup.Basic
public import Mathlib.GroupTheory.Index
public import Mathlib.Topology.Algebra.Group.Quotient
/-!
# Closed subgr... |
1,926 | lean_file_chunk | bf14fc156f15742006eea921d131c2b1570e6f1f008259aff82d2e3a8eef5766 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 María Inés de Frutos-Fernández. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: María Inés de Frutos-Fernández
-/
module
public import Mathlib.GroupTheory.Commutator.Basic
public import Mathlib.Tactic.Group
public import Mathlib.Topology.Algebra.G... |
2,665 | lean_file_chunk | 49f0f750af552cb71a3a95309e8a9c145d2fcf69415e607dfc6516fd77d852a4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Ruben Van de Velde. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ruben Van de Velde, David Ledvinka
-/
module
public import Mathlib.Algebra.Group.Pi.Units
public import Mathlib.Algebra.Group.Submonoid.Units
public import Mathlib.Topology.Algebr... |
3,615 | lean_file_chunk | 5ce9a4c0d772522acd58ad1f57dba06c29af7789624b0f65a1a962690954cdeb | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Michael Rothgang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Rothgang
-/
module
public import Mathlib.Algebra.Module.Shrink
public import Mathlib.Topology.Algebra.Module.Equiv
public import Mathlib.Topology.Instances.Shrink
public imp... |
1,597 | lean_file_chunk | fdcadd7fd03bcbdaf37ed6772124f8a6c0e6119af157a1929a7d590deb9cb5cb | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.LinearAlgebra.Finsupp.LinearCombination
public import Mathlib.RingTheory.Finiteness.Defs
public import Mathlib.Topology.Algebra.Ring.Basic
pub... |
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