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 |
|---|---|---|---|---|---|
4,116 | lean_file_chunk | b2ca1ab0ed2dceef7c47a3ec860031a4112284516a2e82d3236c086829212a2d | 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, Frédéric Dupuis
-/
module
public import Mathlib.Algebra.Star.Module
public import Mathlib.Topology.Algebra.Module.Equiv
public import Mathlib.Topology.Algebra.Star
/-!
# Th... |
3,125 | lean_file_chunk | a1581f8c68531f0ce973908bbee5d1b6a3d29801477367bea711cae864ff90a4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Yaël Dillies, Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Andrew Yang
-/
module
public import Mathlib.LinearAlgebra.BilinearMap
public import Mathlib.Topology.Algebra.Module.LinearMap
/-!
# Continuous perfect pairin... |
1,812 | lean_file_chunk | 541de26d1e1998fd33e2f5d3bcf2eabfac0b29097c900f5392bc55f491f35f52 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Bjørn Solheim. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bjørn Solheim
-/
module
public import Mathlib.LinearAlgebra.Dual.Lemmas
public import Mathlib.Topology.Algebra.Module.FiniteDimension
public import Mathlib.Topology.Algebra.Module.Perf... |
13,870 | lean_file_chunk | 74741d253210483e83c5b46a60ac85edc5269e61b11a46a4f261d146237ef2a7 | 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.Topology.Algebra.Module.Equiv
public import Mathlib.Topology.Sets.Closeds
/-!
# Closed submodules of a topological module
This file builds... |
3,031 | lean_file_chunk | 728dc6b22a1d5d94f893726f917f6f12c7f60b10ecd6672fbc043c9379718112 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Michael Rothgang
-/
module
public import Mathlib.Topology.Algebra.Module.FiniteDimension
public import Mathlib.Topology.Algebra.Module.Spaces.ContinuousLinearMap
/-!
... |
1,271 | lean_file_chunk | 69bf09d40f8ff46852abd9e1c822dd318c4023d3468625afec2f3c43ae364ef8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
module
public import Mathlib.Analysis.SpecificLimits.Normed
public import Mathlib.Topology.Perfect
/-! # Vector spaces over nontrivially normed fields are per... |
14,389 | lean_file_chunk | dd23c30fc35b50c557c8c7558ab045fb2d1e99fffb232197c355bff17a3a4767 | 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: Jan-David Salchow, Sébastien Gouëzel, Jean Lo, Yury Kudryashov, Frédéric Dupuis,
Heather Macbeth
-/
module
public import Mathlib.Algebra.Module.Opposite
public import Mathlib.Top... |
23,966 | lean_file_chunk | 20ec064ed822450ef87ff697464765553ab4ec29126ef370247ccc024f07e247 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Anatole Dedecker
-/
module
public import Mathlib.Analysis.LocallyConvex.BalancedCoreHull
public import Mathlib.Analysis.LocallyConvex.Bounded
public import Mathli... |
7,555 | lean_file_chunk | 5269a9c5727a63f3f2f69a609754e33547ca8f7fdb1e598cf8c6507b76f7e219 | lean_source_file | pkg_mathlib_source_file_chunks | [T2Space E] (s : Submodule 𝕜 E) [FiniteDimensional 𝕜 s] :
IsClosed (s : Set E) :=
letI := IsTopologicalAddGroup.rightUniformSpace E
haveI : IsUniformAddGroup E := isUniformAddGroup_of_addCommGroup
s.complete_of_finiteDimensional.isClosed
/-- An injective linear map with finite-dimensional domain is a close... |
5,822 | lean_file_chunk | 3abe0d0c6e9be3805d42b956ff3ca6596885c0c6bd02e4255dbb6b3d3c29645f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker
-/
module
public import Mathlib.Analysis.LocallyConvex.Bounded
public import Mathlib.Topology.Algebra.FilterBasis
public import Mathlib.Topology.Algebra.UniformConv... |
6,815 | lean_file_chunk | 9dc872758777ffcb8ba1e8774e2ac9a3a20fa571af78c53f30536d240b2d0a83 | 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.Algebra.Module.Card
public import Mathlib.Analysis.SpecificLimits.Normed
public import Mathlib.SetTheory.Cardinal.Continuum
public... |
12,957 | lean_file_chunk | 945828609da3b6957077c3d1d6b53b479266035bf9f74fb242f32721d4550fe5 | 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: Jan-David Salchow, Sébastien Gouëzel, Jean Lo, Yury Kudryashov, Frédéric Dupuis,
Heather Macbeth
-/
module
public import Mathlib.Topology.Algebra.Module.LinearMap
/-!
# Continuo... |
1,358 | lean_file_chunk | 2d79a09d6af34d23cbf3fc92a56237ff3bb4617069a71c9c72ac3591fd98ae15 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker
-/
module
public import Mathlib.RingTheory.SimpleModule.Basic
public import Mathlib.Topology.Algebra.Module.Basic
/-!
# The kernel of a linear function is closed o... |
217 | lean_file_chunk | 5a261519bb42220dc74c7e67d18ccfe727c5e0856a8f155301f20f55791ffa89 | lean_source_file | pkg_mathlib_source_file_chunks | module -- shake: keep-all
public import Mathlib.Topology.Algebra.Module.Spaces.ContinuousLinearMap
public import Mathlib.Topology.Algebra.Module.Spaces.CompactConvergenceCLM
deprecated_module (since := "2026-04-01") |
23,982 | lean_file_chunk | 9194e6023ab2337bdd80af534e310ae63f83fd84d96643cee7feab6c059046e8 | 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: Jan-David Salchow, Sébastien Gouëzel, Jean Lo, Yury Kudryashov, Frédéric Dupuis,
Heather Macbeth
-/
module
public import Mathlib.Algebra.Module.LinearMap.DivisionRing
public impo... |
23,984 | lean_file_chunk | 3e0f77c7df97038a464c26bb302ea9da07ca653f228072eef4f15328429face8 | lean_source_file | pkg_mathlib_source_file_chunks | [AddCommMonoid M'] [Module R₁ M'] [T2Space M₂]
(f g : M' →SL[σ₁₂] M₂) : CompleteSpace (LinearMap.eqLocus f g) :=
IsClosed.completeSpace_coe (hs := isClosed_eq (map_continuous f) (map_continuous g))
/-- Restrict codomain of a continuous linear map. -/
def codRestrict (f : M₁ →SL[σ₁₂] M₂) (p : Submodule R₂ M₂) (h ... |
2,316 | lean_file_chunk | 6ade3ed7fe34711782712b4f4b67b9d866a352381429240495487b61926bac72 | lean_source_file | pkg_mathlib_source_file_chunks | simpa [← ContinuousLinearMap.coe_comp] using
LinearMap.IsIdempotentElem.ker_mem_invtSubmodule_iff (T := T) hf.toLinearMap
alias ⟨IsIdempotentElem.conj_eq_of_ker_mem_invtSubmodule,
IsIdempotentElem.ker_mem_invtSubmodule⟩ := IsIdempotentElem.ker_mem_invtSubmodule_iff
/-- An idempotent operator `f` commutes with `... |
23,973 | lean_file_chunk | cda3b261068b119d748901959e01b3babfe127feff02d45364d4597df25cccb7 | 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: Jan-David Salchow, Sébastien Gouëzel, Jean Lo, Yury Kudryashov, Frédéric Dupuis,
Heather Macbeth
-/
module
public import Mathlib.Topology.Algebra.Module.LinearMapPiProd
/-!
# Co... |
23,985 | lean_file_chunk | 1680e542ff2a930b2c61fc82ed5c72773836d46c76486ead48b5b122d0e7672d | lean_source_file | pkg_mathlib_source_file_chunks | (equivOfInverse f₁ f₂ h₁ h₂).symm = equivOfInverse f₂ f₁ h₂ h₁ :=
rfl
/-- Create a `ContinuousLinearEquiv` from two `ContinuousLinearMap`s that are
inverse of each other, in the `ContinuousLinearMap.comp` sense. See also `equivOfInverse`. -/
def equivOfInverse' (f₁ : M₁ →SL[σ₁₂] M₂) (f₂ : M₂ →SL[σ₂₁] M₁)
(h₁ : f... |
6,102 | lean_file_chunk | 883a41c1b38679199d781b2023ae637db2fa84887606b61bb9fb3452c153f2e5 | lean_source_file | pkg_mathlib_source_file_chunks | continuous_toFun := by
have h' : (fun x ↦ x ∈ p) = (fun x ↦ x ∈ q) := by simp [h]
exact (Homeomorph.ofEqSubtypes h').continuous
continuous_invFun := by
have h' : (fun x ↦ x ∈ p) = (fun x ↦ x ∈ q) := by simp [h]
exact (Homeomorph.ofEqSubtypes h').symm.continuous
/--
A continuous linear equivalence of ... |
9,108 | lean_file_chunk | 533204136e120345b411c19c55c9a5a66d67bc6399e6fb487021d0c945d5f6e6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Moritz Doll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Doll
-/
module
public import Mathlib.LinearAlgebra.LinearPMap
public import Mathlib.Topology.Algebra.Module.Basic
public import Mathlib.Topology.Algebra.Module.Equiv
/-!
# Partia... |
1,772 | lean_file_chunk | 504eb45750a20eb6f1b0bc3199da5fdd295bc813596ed681ae7c04bc2f52096c | 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: Jan-David Salchow, Sébastien Gouëzel, Jean Lo, Yury Kudryashov, Frédéric Dupuis,
Heather Macbeth
-/
module
public import Mathlib.Topology.Algebra.Module.Equiv
public import Mathl... |
23,996 | lean_file_chunk | 180430d5c992cf7a778ba818331e37fade248ae370f099fef46b95b54843e533 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, Will Sawin
-/
module
public import Mathlib.Topology.Algebra.Module.Equiv
public import Mathlib.RingTheory.Finiteness.Cardinality
public import Mathlib.Algebra.Algebra.Bi... |
10,228 | lean_file_chunk | 8a60806a260abf19d5519220df6acfd6b38ef9e54e6bb8d4df9f99a32ec849e6 | lean_source_file | pkg_mathlib_source_file_chunks | have hOpenMap :=
letI : TopologicalSpace A := moduleTopology R A
have : IsModuleTopology R A := ⟨rfl⟩
isOpenQuotientMap_of_surjectiveₛₗ hσ φ hφ |>.isOpenMap
intro U hU
exact hOpenMap U <| moduleTopology_le R A U hU
omit [IsModuleTopology R A] in
/-- A linear surjection to a module with the module topol... |
11,641 | lean_file_chunk | 4b558760f3c41e76af69600ebe6d2eb3202e0e567220aa8030f0a512279c58f0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker
-/
module
public import Mathlib.Analysis.Convex.Topology
public import Mathlib.Topology.Connected.LocPathConnected
public import Mathlib.Analysis.Convex.PathConnect... |
5,547 | lean_file_chunk | a93638a48628b49bee2ef157d5d4f0fc2ca1fd9c8d3b737f564924cbfda5cceb | 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.Homeomorph.Lemmas
public import Mathlib.GroupTheory.GroupAction.DomAct.Basic
/-!
# Topological space structure on `Mᵈᵐᵃ` and... |
6,171 | lean_file_chunk | 77295c3cda5ec34ac709787110606a886f565ab9f19bb0392ac8905d61934f5b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 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.Algebra.Order.Field
public import Mathlib.Topology.MetricSpace.Lipschitz
/-!
# Lipschitz continuous functions
This file... |
4,620 | lean_file_chunk | 0ce6f4aeb68af5b8f7e2dfbf01117bea041efb20e18c84335ed53601b81b9383 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
module
public import Mathlib.Algebra.Star.LinearMap
public import Mathlib.Topology.Algebra.Module.Star
/-! # Intrinsic star operation on continuous linear maps
This file... |
1,300 | lean_file_chunk | fcc11c3b4cbb9210f5710138586020a3db693de47faaadd069a43a359b9362fb | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux, Bhavik Mehta
-/
module
public import Mathlib.Algebra.Star.Unitary
public import Mathlib.Topology.Algebra.Group.Defs
public import Mathlib.Topology.Algebra.Star
public im... |
653 | lean_file_chunk | a986d07b46a153dcc8cf2bd5f17dd2e7af65cee588391e52352df67661a9163a | 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.NNReal.Star
public import Mathlib.Topology.Algebra.Star
public import Mathlib.Topology.MetricSpace.Pseudo.Construct... |
3,720 | lean_file_chunk | 6d083734918c8baae98abe36696607cc5053bf284539a6cfe837f08905c1d6e7 | 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.Commensurable
public import Mathlib.Topology.Algebra.ContinuousMonoidHom
public import Mathlib.Topology.Algebra.Group.Closed... |
1,938 | lean_file_chunk | 1b6ff7b6208cd0d2f7e750838e3de1cf41809e689f42d9d9bbaaa658031ce341 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck
-/
module
public import Mathlib.Topology.Algebra.IsUniformGroup.Defs
public import Mathlib.Topology.Order.Basic
public import Mathlib.Topology.UniformSpace.UniformConve... |
23,990 | lean_file_chunk | fb90480b397622f91133ec0f1ef64ff6be7f8217764b65d11109b9ab84ec22c2 | 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.UniformSpace.UniformConvergence
public import Mathlib.Topology.UniformSpace.CompleteSeparated
public import Mat... |
12,748 | lean_file_chunk | e42b7ae0a16abb5e54e40eec101054056840f102686c9fb69777e46de88026ba | lean_source_file | pkg_mathlib_source_file_chunks | have h₄ := H x₁ x₁_in x xU₁ y yV₁ y' y'V₁
exact W4 h₁ h₂ h₃ h₄
open IsDenseInducing
variable [T0Space G] [CompleteSpace G]
/-- Bourbaki GT III.6.5 Theorem I:
ℤ-bilinear continuous maps from dense images into a complete Hausdorff group extend by continuity.
Note: Bourbaki assumes that α and β are also complete Haus... |
3,033 | lean_file_chunk | 8e2bed94098535bcbbb1d0974ef2926ca0e89bdec1570038949b6da908404833 | 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, Patrick Massot, Johannes Hölzl
-/
module
public import Mathlib.Topology.Algebra.IsUniformGroup.Defs
public import Mathlib.Topology.UniformSpace.Pi
public import Ma... |
23,906 | lean_file_chunk | b529ba46685cf82df5d3c9d0b478f87a85886a2f5ef28764d8de722d496c1895 | 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, Anatole Dedecker
-/
module
public import Mathlib.Topology.UniformSpace.Basic
public import Mathlib.Topology.Algebra.Group.Basic
/-!
# Uniform structur... |
6,857 | lean_file_chunk | 706b5564302dde0f8822e09e56ba534f81853f6f4c6b449ab72d40f079bd88e0 | lean_source_file | pkg_mathlib_source_file_chunks | @[to_additive /-- A homomorphism from a uniform additive group to a discrete uniform additive group
is continuous if and only if its kernel is open. -/]
theorem IsUniformGroup.uniformContinuous_iff_isOpen_ker {hom : Type*} [UniformSpace β]
[DiscreteTopology β] [Group β] [IsUniformGroup β] [FunLike hom α β] [MonoidH... |
847 | lean_file_chunk | 1514e6c56dab12070ae670dd1db4fb9339ae60c7260b6447ef1b2b7b26e04542 | 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.AddTorsor
public import Mathlib.Topology.Algebra.ProperAction.Basic
/-!
# The action underlying a topologica... |
4,308 | lean_file_chunk | d1172a3dd41a65950bc4ba12bbe45fff88188def9da634457e9b416e2345f3ad | 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: Etienne Marion
-/
module
public import Mathlib.Topology.Algebra.ProperAction.Basic
public import Mathlib.Topology.Compactness.CompactlyGeneratedSpace
public import Mathlib.Topology.Ma... |
14,427 | lean_file_chunk | c62f6201020f6cdf510fe50702bb797b35a11f22f0a6e716a72fbfdd8f542461 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Anatole Dedeker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedeker, Etienne Marion, Florestan Martin-Baillon, Vincent Guirardel
-/
module
public import Mathlib.Topology.Algebra.Group.Quotient
public import Mathlib.Topology.Algebra.Mu... |
140 | lean_file_chunk | be4dda9b63182ebe153218e6c27361d029fe1aabf31df857937626cc1c1dff99 | lean_source_file | pkg_mathlib_source_file_chunks | module -- shake: keep-all
public import Mathlib.Topology.Algebra.ProperAction.CompactlyGenerated
deprecated_module (since := "2026-03-21") |
5,707 | lean_file_chunk | 6946fd571b20b372202b2e88d9fc78d35e7726833e21bb731d3b9b3d7672a660 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.RingTheory.DedekindDomain.Factorization
public import Mathlib.RingTheory.DiscreteValuationRing.Basic
public import Mathlib.RingTheory.HopkinsL... |
23,983 | lean_file_chunk | 255960ba713ce6c7c1465e74c40b39d8b124e22c0599fdb73fbe39f15d3b473f | 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.Order.AbsoluteValue.Basic
public import Mathlib.Algebra.Ring.Opposite
public import Mathlib.Algebra.Ring.Prod
pu... |
1,392 | lean_file_chunk | 7214af81b96fc8d484bbe469ef961e5297c4f2b6780049ed6ed06202866c6dca | lean_source_file | pkg_mathlib_source_file_chunks | theorem coinduced_continuous {R S : Type*} [t : TopologicalSpace R] [Ring S] (f : R → S) :
Continuous[t, (coinduced f).toTopologicalSpace] f :=
continuous_sInf_rng.2 <| forall_mem_image.2 fun _ => continuous_iff_coinduced_le.2
/-- The forgetful functor from ring topologies on `a` to additive group topologies on ... |
3,125 | lean_file_chunk | daca316fa16330a8bc318eac95770d47e3918d73d6af1cffc45f769bbef6acd0 | 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
-/
module
public import Mathlib.Topology.Algebra.Ring.Basic
public import Mathlib.Topology.Algebra.Group.Quotient
public import Mathlib.RingTheory.Ideal.Quotient.Defs
... |
4,344 | lean_file_chunk | a3c0f5f569fbea430788d7369d5446e3ae1d2efde947f6bb507f7c3de8351184 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
module
public import Mathlib.Data.EReal.Operations
public import Mathlib.Topology.Algebra.Order.Field
public import Mathlib.Topology.Algebra.IsUnifor... |
2,403 | lean_file_chunk | b36f647b7ea947513a54fcd8ed5216c8d0a0ec4dc00fd141511154d10f60fcfe | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Mitchell Lee. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mitchell Lee
-/
module
public import Mathlib.Topology.Algebra.GroupCompletion
public import Mathlib.Topology.Algebra.InfiniteSum.Group
/-!
# Infinite sums in the completion of a topolo... |
9,464 | lean_file_chunk | 46fb0025570f039b9f148f2f596d91faba79db5d04f8f569cf3b11ab48d451da | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Fengyang Wang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fengyang Wang
-/
module
public import Mathlib.Topology.Algebra.InfiniteSum.Basic
public import Mathlib.Topology.Algebra.InfiniteSum.Constructions
public import Mathlib.Topology.Algebra... |
23,796 | lean_file_chunk | d1aa0bb14fa6c62650fcc26abc03fe395a5de9c622a14645b011faf49ca04831 | 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.Group.EvenFunction
public import Mathlib.Logic.Encodable.Lattice
public import Mathlib.Order.Filter.AtTopBot.Finset
public impor... |
23,977 | lean_file_chunk | b7e31ed72730bfeba6e39d96704ed525add0ec619ab33a50f1c845584670071e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Edward van de Meent. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Edward van de Meent
-/
module
public import Mathlib.Data.Real.ENatENNReal
public import Mathlib.Data.Set.Card
public import Mathlib.Topology.Instances.ENNReal.Lem... |
5,085 | lean_file_chunk | 956aa0f29b0f527fb8b3241914100c59c234564317dc48273fcb882800e90437 | lean_source_file | pkg_mathlib_source_file_chunks | rw [lt_top_iff_ne_top, ENNReal.tsum_coe_ne_top_iff_summable]
exact hf.toNNReal
lemma Summable.tsum_ofReal_ne_top {f : α → ℝ} (hf : Summable f) : ∑' i, .ofReal (f i) ≠ ∞ :=
hf.tsum_ofReal_lt_top.ne
/-- Finitely summable non-negative functions have countable support -/
theorem _root_.Summable.countable_support_ennr... |
11,541 | lean_file_chunk | 1a6403f00c297f24aef26331547b8fc056a13efbf80e118c747a033e0b218063 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth, Yury Kudryashov, Frédéric Dupuis
-/
module
public import Mathlib.Topology.Algebra.InfiniteSum.Constructions
public import Mathlib.Topology.Algebra.Module.Equiv
/-! ... |
14,293 | lean_file_chunk | 25850c2d10c92096d52dc01c4ecf20d47a7be9a13e742d6dc081f899dca02cb9 | 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.NatAntidiagonal
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Algebra.Ring.GeomSum
p... |
19,105 | lean_file_chunk | 037e780a1c9feabe59a7e1598ca325cff2e608d8b78fcf3bded280cec6ae8f56 | 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.SetTheory.Cardinal.Finite
public import Mathlib.Topology.Algebra.InfiniteSum.Basic
public import Mathlib.Topology.UniformSpace.Cauchy
pu... |
5,458 | lean_file_chunk | e2f68e2ddca32463a16402ee71dba061e6d3592c34abcaa4294c4aaf694c9d02 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck
-/
module
public import Mathlib.Analysis.Calculus.IteratedDeriv.Defs
public import Mathlib.Analysis.Calculus.UniformLimitsDeriv
public import Mathlib.Analysis.Normed.Gr... |
15,043 | lean_file_chunk | 11d01e633916121c7d6dba23bd98baa51613d7920b920beab0929b2925d5f6e2 | 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.Order.Archimedean.Basic
public import Mathlib.Algebra.Order.BigOperators.Ring.Finset
public import Mathlib.Topology.Algebra.Infi... |
23,997 | lean_file_chunk | b82da99c1e5dd7018ddd73dedecf25c904d5e32efcc0046a962b1c83e452c952 | 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, Mitchell Lee
-/
module
public import Mathlib.Algebra.BigOperators.Group.Finset.Indicator
public import Mathlib.Algebra.FiniteSupport.Defs
public import Mathlib.Algebra... |
9,310 | lean_file_chunk | 4cc6430b4682f2a27e18dca267e27992d324d0ed9fe8a2cbac17723f25f84745 | lean_source_file | pkg_mathlib_source_file_chunks | theorem tprod_subtype_eq_of_mulSupport_subset {f : β → α} {s : Set β} (hs : mulSupport f ⊆ s) :
∏' x : s, f x = ∏' x, f x :=
Subtype.val_injective.tprod_eq <| by simpa
@[to_additive]
theorem tprod_subtype_mulSupport (f : β → α) : ∏' x : mulSupport f, f x = ∏' x, f x :=
tprod_subtype_eq_of_mulSupport_subset Set... |
13,398 | lean_file_chunk | 1f2428619b11ed2e56ede66336cab63a821be3e2aa6c0617987983227194cb8f | 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.Order.Filter.AtTopBot.Finset
public import Mathlib.Topology.Algebra.InfiniteSum.Group
public import Mathlib.Topology.Algebra.Star
/-!
#... |
20,828 | lean_file_chunk | 5f237ca78cfdfe2e8ee470ff5c4af8fab49b94812eafb3942a56a3b1c0208b01 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck, David Loeffler, Andrew Yang
-/
module
public import Mathlib.Topology.Algebra.InfiniteSum.Defs
public import Mathlib.Topology.Algebra.UniformConvergence
public import M... |
15,912 | lean_file_chunk | f3de986e2df6340c026af4c92ad58dab683a57b17fe72ebf4abcba898d883ee1 | 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.Finprod
public import Mathlib.Topology.Algebra.InfiniteSum.SummationFilter
public import Mathlib.Topology.Separatio... |
7,679 | lean_file_chunk | d1a1a2151c6fdb90994282234a7cf58aa26487d128ecf386d2695864dab3dc43 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck
-/
module
public import Mathlib.Algebra.BigOperators.Group.Finset.Interval
public import Mathlib.Analysis.Normed.Group.Int
public import Mathlib.Analysis.Normed.Group.U... |
1,032 | lean_file_chunk | aade837557bbbc49bc1e0a7096281f50be45b97071ba5c3d7d7b3747a20c5899 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
module
public import Mathlib.Analysis.Normed.Group.Continuity
public import Mathlib.Analysis.Normed.Ring.Basic
public import Mathlib.Topology.Algebra.InfiniteSum.Defs
/... |
10,931 | lean_file_chunk | ad20b8a6a83e0503490d975ab958888e22b985604ed67327e568f675a26cc68c | 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.Data.Finset.Preimage
public import Mathlib.Order.Filter.AtTopBot.CountablyGenerated
public import Mathlib.Order.Interval.Finset.Nat
publ... |
7,228 | lean_file_chunk | 9eaf2bbbeafe386f302723671cd6dcace45620772c2f7d59e2ce521b982c18d1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Mitchell Lee. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mitchell Lee
-/
module
public import Mathlib.Algebra.Group.Subgroup.Finite
public import Mathlib.Topology.Algebra.InfiniteSum.GroupCompletion
public import Mathlib.Topology.Algebra.Infi... |
5,437 | lean_file_chunk | e20740f788cd015a11aea238e714291e6e2fc613c26d6a31f9c79373beec1e63 | 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.Algebra.BigOperators.Intervals
public import Mathlib.Topology.Algebra.InfiniteSum.Order
public import Mathlib.Top... |
13,490 | lean_file_chunk | 0ad6850914973f46537628eb1c9f89d47be119d2ce2f0e13f664bfcf70e4f39f | 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.Algebra.Algebra.Basic
public import Mathlib.Topology.Algebra.FilterBasis
public import Mathlib.Topology.Algebra.Nonarchimedean.Basic
/-... |
2,168 | lean_file_chunk | 980a5dcbca535022ce81d23acea6d4893d55ede07bda7a056936d89da49da7dc | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Jou Glasheen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jou Glasheen, Kevin Buzzard, David Loeffler, Yongle Hu, Johan Commelin
-/
module
public import Mathlib.Topology.Algebra.Nonarchimedean.Basic
/-!
# Total separatedness of nonarchimedean... |
3,290 | lean_file_chunk | e4a2aede0b45312c8ce9346509d98071ad3f10694a1059fd3388a89f3e20f8d9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Mitchell Lee. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mitchell Lee
-/
module
public import Mathlib.Topology.Algebra.Nonarchimedean.Basic
public import Mathlib.Topology.Algebra.GroupCompletion
public import Mathlib.Topology.Algebra.UniformR... |
5,939 | lean_file_chunk | e9275a00d1522669247a554299d055223a46d8a92468850400ac9eea248b066a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Ashwin Iyengar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, Johan Commelin, Ashwin Iyengar, Patrick Massot
-/
module
public import Mathlib.Algebra.Group.Subgroup.Basic
public import Mathlib.Topology.Algebra.OpenSubgroup
public i... |
11,407 | lean_file_chunk | 722d859c3dad2f29b749b184cd4af39e3b55465ce68ab54502f41a24df30ad0e | 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.RingTheory.Ideal.Maps
public import Mathlib.Topology.Algebra.IsUniformGroup.Defs
public import Mathlib.Topology.Algebra.Nonarchimedean.B... |
23,924 | lean_file_chunk | 2a0007c12685444af3612c6bda026459359319054970b2f10b4d855356d8aa1f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Salvatore Mercuri. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Salvatore Mercuri
-/
module
public import Mathlib.Algebra.Algebra.TransferInstance
public import Mathlib.Algebra.Field.TransferInstance
public import Mathlib.RingTheory.Valuation.V... |
1,208 | lean_file_chunk | 039a675ae1a2ceb175c54e3ad204615ffb4e315f79af3bdd7693613ecb71336d | lean_source_file | pkg_mathlib_source_file_chunks | (Valued.isClopen_closedBall _ one_ne_zero) (Valued.isClopen_closedBall _ one_ne_zero)
rw [restrict_le_one_iff]
rfl
| ih a =>
simpa [Valued.valuedCompletion_apply] using h.le_one_iff_le_one
end Equivalence
end Valuation
namespace NumberField.RingOfIntegers
variable {K : Type*} [Field K] [NumberField K]... |
10,802 | lean_file_chunk | 7138bab301a19e72fff668986b586cbced465ea890e0b80e43a24ee9e9eb9bba | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 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, Filippo A. E. Nuccio
-/
module
public import Mathlib.Analysis.Normed.Field.Basic
public import Mathlib.Analysis.Normed.Group.Ultra
publ... |
15,668 | lean_file_chunk | 58b85eb3463ad64627aaa8b2b9ad1cf79a3edf8684138f2c9b3146ed1355ddd2 | 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.Analysis.Normed.Field.Lemmas
public import Mathlib.Analysis.Normed.Field.ProperSpace
public import Mathlib.RingTheory.DiscreteValuatio... |
3,105 | lean_file_chunk | 8d94ea98ff3663a2d3366ba016dcce50a1855d3ba7334ba234ccb0d8ce31b8bf | 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.Algebra.ValuativeRel.ValuativeTopology
/-!
# Valuative Relations as Valued
In this temporary file, we provide a helper ins... |
1,949 | lean_file_chunk | 78dcbc8824ee58d55e704607288be7f345c1fef1c071c2b3e19df3d9f587f00e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Salvatore Mercuri. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Salvatore Mercuri
-/
module
public import Mathlib.GroupTheory.ArchimedeanDensely
public import Mathlib.Topology.Algebra.Valued.ValuationTopology
/-!
# Topological results for inte... |
14,294 | lean_file_chunk | ac61276cba9fc5e7c9d0dcace7738ba8845be798a3dddee54a0b8873c7881903 | 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.Algebra.Order.Group.Units
public import Mathlib.Topology.Algebra.Nonarchimedean.Bases
public import Mathlib.Topology.Algebra.UniformFilt... |
23,965 | lean_file_chunk | 0c9a65628e56cb4fdf5b34137de4fe477d8c3cc384bfc30b2cf65fb21b2aa19c | 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.Valued.ValuationTopology
public import Mathlib.Topology.Algebra.WithZeroTopology
public import Mathlib.Topology.Algebra... |
4,880 | lean_file_chunk | 2d3b51130dc75250f8ff4056f90d701fe26f2cab3adfd34dedc972ac58a20f9b | lean_source_file | pkg_mathlib_source_file_chunks | fun γ : (ValueGroup₀ hv.v)ˣ => { x | extensionValuation x <
(Units.map (ValueGroup₀.embedding (f := hv.v)) γ).1 } by
rw [this.mem_iff]
simp only [extensionValuation_toFun, Units.coe_map, MonoidHom.coe_coe, true_and]
have (x : hat K) (γ : (ValueGroup₀ hv.v)ˣ) : extensionValuation.restrict x <... |
781 | lean_file_chunk | 154d82e4ac580820086860e919292e0f688c056113103b239a7d74f6d338ac7a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.Algebra.Algebra.Rat
public import Mathlib.Topology.Algebra.ConstMulAction
public import Mathlib.Topology.Algebra.Monoid.Defs
/-!
# Topologi... |
12,632 | lean_file_chunk | 1bcecc9607156c3cb661c5c75ce8a5f6831b9888d177f6e3dc18feb1ae250152 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 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.Algebra
public import Mathlib.Topology.Algebra.Module.Equiv
/-!
# Isomorphisms of topological algebras
This fil... |
16,804 | lean_file_chunk | d2929e74249b3bec7e34a98afeb5bf5e711538b7d315174a14fcacd1ae8c960c | 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.Algebra.Module.LinearMap
/-!
# Algebraic operations on `SeparationQuotient`
In this file we define algebraic operations (mu... |
3,373 | lean_file_chunk | a807e4450a1967d5902025120e05f9f1f57fd841a89994d487111776f27a3ca5 | 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.Module.Projective
public import Mathlib.LinearAlgebra.Basis.VectorSpace
public import Mathlib.Topology.Algebra.SeparationQuoti... |
1,571 | lean_file_chunk | 5b13cb1f123ff6afd33210d5c78bf840ea337cfedb2d49f720354150ea940c0b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Yoh Tanimoto. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yoh Tanimoto
-/
module
public import Mathlib.Topology.Algebra.ContinuousMonoidHom
public import Mathlib.Topology.Algebra.SeparationQuotient.Basic
/-!
# Lift of `MonoidHom M N` to `Mono... |
834 | lean_file_chunk | 97fb53caaa9e9504856be4d5bb1a40bf8d2b16e0ba70a6f33ae575c5459c9428 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Topology.Algebra.SeparationQuotient.Basic
public import Mathlib.RingTheory.Finiteness.Basic
/-!
# Separation quotient is a finite mod... |
17,232 | lean_file_chunk | f8a74d1d095ef9714c393ba2b613233011041cacaca2d5b6d54cc8bb7c3e9bd8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Jiedong Jiang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jiedong Jiang
-/
module
public import Mathlib.RingTheory.Valuation.ValuativeRel.Basic
public import Mathlib.Topology.Algebra.Valued.ValuationTopology
public import Mathlib.Topology.Alg... |
7,737 | lean_file_chunk | 780ee946a46ce19175d44af98c03ea968fb194f0f9dbacfb3e4718e8dd24f520 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz
-/
module
public import Mathlib.Algebra.Category.Grp.EpiMono
public import Mathlib.GroupTheory.ResiduallyFinite
public import Mathlib.Topology.Algebra.Category.ProfiniteGrp.Lim... |
15,390 | lean_file_chunk | bc7e0f5dd5e9711341a6e7a8d09711488992b84f6813c71dbba4f46ad08f4243 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang, Nailin Guan, Yuyang Zhao
-/
module
public import Mathlib.Algebra.Category.Grp.FiniteGrp
public import Mathlib.Topology.Algebra.Group.ClosedSubgroup
public import Mathlib.T... |
7,245 | lean_file_chunk | cddb9367157eb470442bbfd2a2b7ab9f38a547264cea21986ae0f4c1d30609d4 | 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, Youle Fang, Jujian Zhang, Yuyang Zhao
-/
module
public import Mathlib.CategoryTheory.ConcreteCategory.EpiMono
public import Mathlib.Topology.Algebra.Category.ProfiniteGrp.Ba... |
19,878 | lean_file_chunk | 424f5813ff3060dbb836e6d8e70433a35cdd1a0a78a49aac2b3fb49cef3cb32b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Topology.Algebra.Module.Equiv
public import Mathlib.Topology.Algebra.Module.Multilinear.Bounded
public import Mathlib.Topology.Algebra... |
23,991 | lean_file_chunk | 01d9c5e8a2c874f831c309c03026de30da8aa24e24cf59069951ffacdba5a051 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 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.Algebra.Module.LinearMapPiProd
public import Mathlib.LinearAlgebra.Multilinear.Basic
public import Mathlib.Algebra.BigOpe... |
4,640 | lean_file_chunk | d15aad8b70b368d9a4baa6b98244170bcf863b2f013179a045cab9d5f9dedfcd | lean_source_file | pkg_mathlib_source_file_chunks | toMultilinearMap_injective fun _ _ => rfl
/-- Linear map version of the map `toMultilinearMap` associating to a continuous multilinear map
the corresponding multilinear map. -/
@[simps]
def toMultilinearMapLinear : ContinuousMultilinearMap A M₁ M₂ →ₗ[R'] MultilinearMap A M₁ M₂ where
toFun := toMultilinearMap
map_a... |
4,387 | lean_file_chunk | f2b61e4c7378435ee4b82fb851ff6474b2a2ea45d5ad9da93c8865d7800c7490 | 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.Analysis.LocallyConvex.Bounded
public import Mathlib.Topology.Algebra.Module.Multilinear.Basic
/-!
# Images of (von Neumann) bounded ... |
10,845 | lean_file_chunk | abf3097c6b7be5163fb16ac4fa7fb16dae451cd82eb5f59c8d4f7c3a39d0e7a6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Kalle Kytölä. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kalle Kytölä, Moritz Doll
-/
module
public import Mathlib.LinearAlgebra.BilinearMap
public import Mathlib.Topology.Algebra.Module.LinearMap
public import Mathlib.Topology.Algebra.Module... |
23,907 | lean_file_chunk | 13d77ab0d1aecc0a8affdbd5f6447f42fdb2dd2ee30bbabb3622744f0f19dbbb | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker, Yury Kudryashov
-/
module
public import Mathlib.Topology.Algebra.Module.Spaces.UniformConvergenceCLM
/-!
# Topology of bounded convergence on the space of continu... |
140 | lean_file_chunk | b4c065fffdf807500acee0a250e909047d26a102575ae848a37599eb2e4108df | lean_source_file | pkg_mathlib_source_file_chunks | (e.trans f).conjContinuousAlgEquiv = e.conjContinuousAlgEquiv.trans f.conjContinuousAlgEquiv :=
rfl
end Linear
end ContinuousLinearEquiv |
5,353 | lean_file_chunk | 8b5f66024dc56c4dc882f178058e740873e0c8827f628e33ccff23dc4ab5a87c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker, Yury Kudryashov, Moritz Doll
-/
module
public import Mathlib.Topology.Algebra.Module.Spaces.UniformConvergenceCLM
/-!
# Topology of compact convergence on the spa... |
23,108 | lean_file_chunk | c3d250959d495ee1f34bfeba0d6c1420e36a03aea802e8b33cec7bb6032369a3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker, Yury Kudryashov
-/
module
public import Mathlib.Topology.Algebra.Algebra.Equiv
public import Mathlib.Topology.Algebra.Module.Equiv
public import Mathlib.Topology.A... |
6,108 | lean_file_chunk | ccfe8d7e024c602aa6b398c43eae8ecfce6a8f738366b9d370fceb2eba1a043d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Kalle Kytölä. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kalle Kytölä, Moritz Doll
-/
module
public import Mathlib.Topology.Algebra.Module.LinearMap
public import Mathlib.LinearAlgebra.BilinearMap
/-!
# Weak dual topology
This file defines ... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.