path stringlengths 11 71 | content stringlengths 75 124k |
|---|---|
Topology\Algebra\Field.lean | /-
Copyright (c) 2021 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Scott Morrison
-/
import Mathlib.Algebra.Field.Subfield
import Mathlib.Algebra.GroupWithZero.Divisibility
import Mathlib.Topology.Algebra.GroupWithZero
import Mathlib.T... |
Topology\Algebra\FilterBasis.lean | /-
Copyright (c) 2021 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot
-/
import Mathlib.Order.Filter.Bases
import Mathlib.Topology.Algebra.Module.Basic
/-!
# Group and ring filter bases
A `GroupFilterBasis` is a `FilterBasis` on a group ... |
Topology\Algebra\GroupCompletion.lean | /-
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
-/
import Mathlib.Topology.Algebra.UniformGroup
import Mathlib.Topology.Algebra.UniformMulAction
import Mathlib.Topology.UniformSpace.Completion
/-!
# C... |
Topology\Algebra\GroupWithZero.lean | /-
Copyright (c) 2020 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
import Mathlib.Algebra.Group.Pi.Lemmas
import Mathlib.Topology.Algebra.Monoid
import Mathlib.Topology.Homeomorph
/-!
# Topological group with zero
In this f... |
Topology\Algebra\Localization.lean | /-
Copyright (c) 2021 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
-/
import Mathlib.GroupTheory.MonoidLocalization.Basic
import Mathlib.RingTheory.OreLocalization.Ring
import Mathlib.Topology.Algebra.Rin... |
Topology\Algebra\Monoid.lean | /-
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
-/
import Mathlib.Algebra.BigOperators.Finprod
import Mathlib.Order.Filter.Pointwise
import Mathlib.Topology.Algebra.MulAction
import Mathlib.Algebra.Big... |
Topology\Algebra\MulAction.lean | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Algebra.AddTorsor
import Mathlib.Topology.Algebra.Constructions
import Mathlib.GroupTheory.GroupAction.SubMulAction
import Mathlib.Topology.Algebra.C... |
Topology\Algebra\MvPolynomial.lean | /-
Copyright (c) 2023 Ruben Van de Velde. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ruben Van de Velde
-/
import Mathlib.Algebra.MvPolynomial.Basic
import Mathlib.Topology.Algebra.Ring.Basic
/-!
# Multivariate polynomials and continuity
In this file we prove th... |
Topology\Algebra\OpenSubgroup.lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import Mathlib.RingTheory.Ideal.Basic
import Mathlib.Topology.Algebra.Ring.Basic
import Mathlib.Topology.Sets.Opens
/-!
# Open subgroups of a topological groups
Thi... |
Topology\Algebra\Polynomial.lean | /-
Copyright (c) 2018 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis
-/
import Mathlib.Algebra.Polynomial.AlgebraMap
import Mathlib.Algebra.Polynomial.Inductions
import Mathlib.Algebra.Polynomial.Splits
import Mathlib.Analysis.Normed.Fi... |
Topology\Algebra\PontryaginDual.lean | /-
Copyright (c) 2022 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
import Mathlib.Analysis.SpecialFunctions.Complex.Circle
import Mathlib.Topology.Algebra.ContinuousMonoidHom
/-!
# Pontryagin dual
This file defines the Pontryagin... |
Topology\Algebra\ProperAction.lean | /-
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
-/
import Mathlib.Topology.Algebra.Group.Basic
import Mathlib.Topology.Algebra.MulAction
import Mathlib.To... |
Topology\Algebra\ProperConstSMul.lean | /-
Copyright (c) 2023 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Topology.Algebra.ConstMulAction
import Mathlib.Topology.Maps.Proper.Basic
/-!
# Actions by proper maps
In this file we define `ProperConstSMul M X` ... |
Topology\Algebra\Semigroup.lean | /-
Copyright (c) 2021 David Wärn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Wärn
-/
import Mathlib.Topology.Separation
import Mathlib.Algebra.Group.Defs
/-!
# Idempotents in topological semigroups
This file provides a sufficient condition for a semigroup `... |
Topology\Algebra\Star.lean | /-
Copyright (c) 2022 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Algebra.Star.Pi
import Mathlib.Algebra.Star.Prod
import Mathlib.Topology.Algebra.Constructions
import Mathlib.Topology.ContinuousFunction.Basic
/-!
# Contin... |
Topology\Algebra\StarSubalgebra.lean | /-
Copyright (c) 2022 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import Mathlib.Algebra.Star.Subalgebra
import Mathlib.Topology.Algebra.Algebra
import Mathlib.Topology.Algebra.Star
/-!
# Topological star (sub)algebras
A topological... |
Topology\Algebra\UniformConvergence.lean | /-
Copyright (c) 2022 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker
-/
import Mathlib.Topology.Algebra.UniformMulAction
import Mathlib.Algebra.Module.Pi
/-!
# Algebraic facts about the topology of uniform convergence
This file cont... |
Topology\Algebra\UniformField.lean | /-
Copyright (c) 2019 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot
-/
import Mathlib.Algebra.Field.Subfield
import Mathlib.Topology.Algebra.Field
import Mathlib.Topology.Algebra.UniformRing
/-!
# Completion of topological fields
The g... |
Topology\Algebra\UniformFilterBasis.lean | /-
Copyright (c) 2021 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot
-/
import Mathlib.Topology.Algebra.FilterBasis
import Mathlib.Topology.Algebra.UniformGroup
/-!
# Uniform properties of neighborhood bases in topological algebra
This ... |
Topology\Algebra\UniformGroup.lean | /-
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
-/
import Mathlib.Topology.UniformSpace.UniformConvergence
import Mathlib.Topology.UniformSpace.UniformEmbedding
import Mathlib.Topology.UniformSpace.Com... |
Topology\Algebra\UniformMulAction.lean | /-
Copyright (c) 2022 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
import Mathlib.Topology.Algebra.UniformGroup
import Mathlib.Topology.UniformSpace.Completion
/-!
# Multiplicative action on the completion of a uniform space... |
Topology\Algebra\UniformRing.lean | /-
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
-/
import Mathlib.Algebra.Algebra.Defs
import Mathlib.Logic.Equiv.TransferInstance
import Mathlib.Topology.Algebra.GroupCompletion
import Mathlib.Topolog... |
Topology\Algebra\WithZeroTopology.lean | /-
Copyright (c) 2021 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot
-/
import Mathlib.Topology.Algebra.GroupWithZero
import Mathlib.Topology.Order.OrderClosed
/-!
# The topology on linearly ordered commutative groups with zero
Let `Γ₀`... |
Topology\Algebra\Algebra\Rat.lean | /-
Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.Algebra.Algebra.Rat
import Mathlib.Topology.Algebra.Monoid
/-!
# Topological (sub)algebras over `Rat`
## Results
This is just a minimal stub for now... |
Topology\Algebra\Constructions\DomMulAct.lean | /-
Copyright (c) 2024 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Topology.Homeomorph
import Mathlib.GroupTheory.GroupAction.DomAct.Basic
/-!
# Topological structure on `DomMulAct _`
In this file we define topolog... |
Topology\Algebra\Group\Basic.lean | /-
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
-/
import Mathlib.GroupTheory.GroupAction.ConjAct
import Mathlib.GroupTheory.GroupAction.Quotient
import Mathlib.GroupTheory.QuotientGrou... |
Topology\Algebra\Group\Compact.lean | /-
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
-/
import Mathlib.Topology.Algebra.Group.Basic
import Mathlib.Topology.CompactOpen
import Mathlib.Topology.Sets.Compacts
/-!
# Additiona... |
Topology\Algebra\Group\OpenMapping.lean | /-
Copyright (c) 2023 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.Topology.Baire.Lemmas
import Mathlib.Topology.Algebra.Group.Basic
/-! # Open mapping theorem for morphisms of topological groups
We prove that ... |
Topology\Algebra\Group\TopologicalAbelianization.lean | /-
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
-/
import Mathlib.GroupTheory.Abelianization
import Mathlib.Topology.Algebra.Group.Basic
/-!
# The topological abelianization of a group... |
Topology\Algebra\InfiniteSum\Basic.lean | /-
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
-/
import Mathlib.Topology.Algebra.InfiniteSum.Defs
import Mathlib.Data.Fintype.BigOperators
import Mathlib.Topology.Algebra.Monoid
/-!
# Lemmas on infini... |
Topology\Algebra\InfiniteSum\Constructions.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import Mathlib.Topology.Algebra.InfiniteSum.Group
import Mathlib.Topology.Algebra.Star
/-!
# Topological sums and functorial constructions
Lemmas on the interaction... |
Topology\Algebra\InfiniteSum\Defs.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import Mathlib.Topology.Separation
import Mathlib.Algebra.BigOperators.Finprod
/-!
# Infinite sum and product over a topological monoid
This file defines unconditio... |
Topology\Algebra\InfiniteSum\Group.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import Mathlib.Topology.Algebra.InfiniteSum.Basic
import Mathlib.Topology.Algebra.UniformGroup
/-!
# Infinite sums and products in topological groups
Lemmas on topo... |
Topology\Algebra\InfiniteSum\GroupCompletion.lean | /-
Copyright (c) 2024 Mitchell Lee. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mitchell Lee
-/
import Mathlib.Topology.Algebra.GroupCompletion
import Mathlib.Topology.Algebra.InfiniteSum.Group
/-!
# Infinite sums in the completion of a topological group
-/
open U... |
Topology\Algebra\InfiniteSum\Module.lean | /-
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
-/
import Mathlib.Topology.Algebra.InfiniteSum.Constructions
import Mathlib.Topology.Algebra.Module.Basic
/-! # Infinite sums in top... |
Topology\Algebra\InfiniteSum\NatInt.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import Mathlib.Topology.Algebra.InfiniteSum.Group
import Mathlib.Logic.Encodable.Lattice
/-!
# Infinite sums and products over `ℕ` and `ℤ`
This file contains lemma... |
Topology\Algebra\InfiniteSum\Nonarchimedean.lean | /-
Copyright (c) 2024 Mitchell Lee. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mitchell Lee
-/
import Mathlib.Topology.Algebra.InfiniteSum.Group
import Mathlib.Topology.Algebra.Nonarchimedean.Basic
/-!
# Infinite sums and products in nonarchimedean abelian groups
... |
Topology\Algebra\InfiniteSum\Order.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import Mathlib.Algebra.Order.Archimedean.Basic
import Mathlib.Topology.Algebra.InfiniteSum.NatInt
import Mathlib.Topology.Algebra.Order.Field
import Mathlib.Topology.... |
Topology\Algebra\InfiniteSum\Real.lean | /-
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
-/
import Mathlib.Algebra.BigOperators.Intervals
import Mathlib.Topology.Algebra.InfiniteSum.Order
import Mathlib.Topology.Instances.Real
import M... |
Topology\Algebra\InfiniteSum\Ring.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import Mathlib.Algebra.BigOperators.NatAntidiagonal
import Mathlib.Topology.Algebra.InfiniteSum.Constructions
import Mathlib.Topology.Algebra.Ring.Basic
/-!
# Infini... |
Topology\Algebra\Module\Basic.lean | /-
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
-/
import Mathlib.Topology.Algebra.Ring.Basic
import Mathlib.Topology.Algebra.MulA... |
Topology\Algebra\Module\Cardinality.lean | /-
Copyright (c) 2023 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.Algebra.Module.Card
import Mathlib.SetTheory.Cardinal.CountableCover
import Mathlib.SetTheory.Cardinal.Continuum
import Mathlib.Analysis.Specific... |
Topology\Algebra\Module\CharacterSpace.lean | /-
Copyright (c) 2022 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis
-/
import Mathlib.Topology.Algebra.Module.WeakDual
import Mathlib.Algebra.Algebra.Spectrum
import Mathlib.Topology.ContinuousFunction.Algebra
import Mathlib.Data.Set.L... |
Topology\Algebra\Module\Determinant.lean | /-
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
-/
import Mathlib.Topology.Algebra.Module.Basic
import Mathlib.LinearAlgebra.Deter... |
Topology\Algebra\Module\FiniteDimension.lean | /-
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
-/
import Mathlib.Analysis.LocallyConvex.BalancedCoreHull
import Mathlib.LinearAlgebra.FreeModule.Finite.Matrix
import Mathlib.Topology.Algebra.Mo... |
Topology\Algebra\Module\LinearPMap.lean | /-
Copyright (c) 2022 Moritz Doll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Doll
-/
import Mathlib.LinearAlgebra.LinearPMap
import Mathlib.Topology.Algebra.Module.Basic
/-!
# Partially defined linear operators over topological vector spaces
We define bas... |
Topology\Algebra\Module\LocallyConvex.lean | /-
Copyright (c) 2022 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker
-/
import Mathlib.Analysis.Convex.Topology
/-!
# Locally convex topological modules
A `LocallyConvexSpace` is a topological semimodule over an ordered semiring in ... |
Topology\Algebra\Module\Simple.lean | /-
Copyright (c) 2022 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker
-/
import Mathlib.RingTheory.SimpleModule
import Mathlib.Topology.Algebra.Module.Basic
/-!
# The kernel of a linear function is closed or dense
In this file we pro... |
Topology\Algebra\Module\Star.lean | /-
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
-/
import Mathlib.Algebra.Star.Module
import Mathlib.Topology.Algebra.Module.Basic
import Mathlib.Topology.Algebra.Star
/-!
# The star operation, bundled as ... |
Topology\Algebra\Module\StrongTopology.lean | /-
Copyright (c) 2022 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker
-/
import Mathlib.Topology.Algebra.Module.UniformConvergence
/-!
# Strong topologies on the space of continuous linear maps
In this file, we define the strong topo... |
Topology\Algebra\Module\UniformConvergence.lean | /-
Copyright (c) 2022 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker
-/
import Mathlib.Analysis.LocallyConvex.Bounded
import Mathlib.Topology.Algebra.FilterBasis
import Mathlib.Topology.Algebra.UniformConvergence
/-!
# Algebraic fact... |
Topology\Algebra\Module\WeakDual.lean | /-
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
-/
import Mathlib.Topology.Algebra.Module.Basic
import Mathlib.LinearAlgebra.BilinearMap
/-!
# Weak dual topology
This file defines the weak topology given tw... |
Topology\Algebra\Module\Alternating\Basic.lean | /-
Copyright (c) 2023 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Heather Macbeth, Sébastien Gouëzel
-/
import Mathlib.LinearAlgebra.Alternating.Basic
import Mathlib.LinearAlgebra.BilinearMap
import Mathlib.Topology.Algebra.Module.M... |
Topology\Algebra\Module\Multilinear\Basic.lean | /-
Copyright (c) 2020 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.Topology.Algebra.Module.Basic
import Mathlib.LinearAlgebra.Multilinear.Basic
/-!
# Continuous multilinear maps
We define continuous multilinear... |
Topology\Algebra\Module\Multilinear\Bounded.lean | /-
Copyright (c) 2024 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Analysis.LocallyConvex.Bounded
import Mathlib.Topology.Algebra.Module.Multilinear.Basic
/-!
# Images of (von Neumann) bounded sets under continuous ... |
Topology\Algebra\Module\Multilinear\Topology.lean | /-
Copyright (c) 2023 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Topology.Algebra.Module.Multilinear.Bounded
import Mathlib.Topology.Algebra.Module.UniformConvergence
/-!
# Topology on continuous multilinear maps
... |
Topology\Algebra\Nonarchimedean\AdicTopology.lean | /-
Copyright (c) 2021 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot
-/
import Mathlib.RingTheory.Ideal.Maps
import Mathlib.Topology.Algebra.Nonarchimedean.Bases
import Mathlib.Topology.Algebra.UniformRing
/-!
# Adic topology
Given a co... |
Topology\Algebra\Nonarchimedean\Bases.lean | /-
Copyright (c) 2021 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot
-/
import Mathlib.Topology.Algebra.Nonarchimedean.Basic
import Mathlib.Topology.Algebra.FilterBasis
import Mathlib.Algebra.Module.Submodule.Pointwise
/-!
# Neighborhood... |
Topology\Algebra\Nonarchimedean\Basic.lean | /-
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
-/
import Mathlib.Algebra.Group.Subgroup.Basic
import Mathlib.Topology.Algebra.OpenSubgroup
import Mathlib.Topology.Algebr... |
Topology\Algebra\Nonarchimedean\Completion.lean | /-
Copyright (c) 2024 Mitchell Lee. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mitchell Lee
-/
import Mathlib.Topology.Algebra.Nonarchimedean.Basic
import Mathlib.Topology.Algebra.GroupCompletion
import Mathlib.Topology.Algebra.UniformRing
/-!
# The completion of ... |
Topology\Algebra\Order\Archimedean.lean | /-
Copyright (c) 2022 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
import Mathlib.GroupTheory.Archimedean
import Mathlib.Topology.Order.Basic
/-!
# Topology on archimedean groups and fields
In this file we prove the followi... |
Topology\Algebra\Order\Compact.lean | /-
Copyright (c) 2021 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Yury Kudryashov
-/
import Mathlib.Topology.Order.LocalExtr
import Mathlib.Topology.Order.IntermediateValue
import Mathlib.Topology.Support
import Mathlib.Topology.Order... |
Topology\Algebra\Order\Field.lean | /-
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
-/
import Mathlib.Data.Set.Pointwise.Interval
import Mathlib.Topology.Algebra.Field
import Mathlib.Topology.Algebra.Order.... |
Topology\Algebra\Order\Floor.lean | /-
Copyright (c) 2020 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker
-/
import Mathlib.Algebra.Order.Floor
import Mathlib.Topology.Algebra.Order.Group
import Mathlib.Topology.Order.Basic
/-!
# Topological facts about `Int.floor`, `In... |
Topology\Algebra\Order\Group.lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Topology.Algebra.Group.Basic
import Mathlib.Topology.Order.LeftRightNhds
/-!
# Topology on a linear ordered additive commutative group
In this file... |
Topology\Algebra\Order\LiminfLimsup.lean | /-
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
-/
import Mathlib.Algebra.BigOperators.Intervals
import Mathlib.Algebra.BigOperators.Ring
import Mathlib.Algebra.Order.Gro... |
Topology\Algebra\Order\Rolle.lean | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Topology.Order.ExtendFrom
import Mathlib.Topology.Algebra.Order.Compact
import Mathlib.Topology.Order.LocalExtr
import Mathlib.Topology.Order.T5
/-!... |
Topology\Algebra\Order\UpperLower.lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Algebra.Order.UpperLower
import Mathlib.Topology.Algebra.Group.Basic
/-!
# Topological facts about upper/lower/order-connected sets
The topological closu... |
Topology\Algebra\Ring\Basic.lean | /-
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
-/
import Mathlib.Algebra.Order.AbsoluteValue
import Mathlib.Algebra.Ring.Prod
import Mathlib.Algebra.Ring.Subring.Basic
import Mathlib.Topology.Algebra.... |
Topology\Algebra\Ring\Ideal.lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot
-/
import Mathlib.Topology.Algebra.Ring.Basic
import Mathlib.RingTheory.Ideal.Quotient
/-!
# Ideals and quotients of topological rings
In this file we define `Ideal.cl... |
Topology\Algebra\Valued\NormedValued.lean | /-
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
-/
import Mathlib.Analysis.Normed.Field.Basic
import Mathlib.RingTheory.Valuation.RankOne
import Mathlib.Topology.Algebra.Valued.Valuatio... |
Topology\Algebra\Valued\ValuationTopology.lean | /-
Copyright (c) 2021 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot
-/
import Mathlib.Topology.Algebra.Nonarchimedean.Bases
import Mathlib.Topology.Algebra.UniformFilterBasis
import Mathlib.RingTheory.Valuation.ValuationSubring
/-!
# Th... |
Topology\Algebra\Valued\ValuedField.lean | /-
Copyright (c) 2021 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot
-/
import Mathlib.Topology.Algebra.Valued.ValuationTopology
import Mathlib.Topology.Algebra.WithZeroTopology
import Mathlib.Topology.Algebra.UniformField
/-!
# Valued f... |
Topology\Baire\CompleteMetrizable.lean | /-
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
-/
import Mathlib.Analysis.SpecificLimits.Basic
import Mathlib.Topology.Metrizable.Uniformity
/-!
# First Baire theorem
In this file we prove th... |
Topology\Baire\Lemmas.lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.Topology.GDelta
/-!
# Baire spaces
A topological space is called a *Baire space*
if a countable intersection of dense open subsets is dense.
Ba... |
Topology\Baire\LocallyCompactRegular.lean | /-
Copyright (c) 2022 Damien Thomine. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damien Thomine
-/
import Mathlib.Topology.Sets.Compacts
/-!
# Second Baire theorem
In this file we prove that a locally compact regular topological space has Baire property.
-/
open... |
Topology\Bornology\Absorbs.lean | /-
Copyright (c) 2020 Jean Lo, Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean Lo, Yury Kudryashov
-/
import Mathlib.Data.Set.Pointwise.SMul
import Mathlib.Topology.Bornology.Basic
/-!
# Absorption of sets
Let `M` act on `α`, let `A` and `B` be s... |
Topology\Bornology\Basic.lean | /-
Copyright (c) 2022 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import Mathlib.Order.Filter.Cofinite
/-!
# Basic theory of bornology
We develop the basic theory of bornologies. Instead of axiomatizing bounded sets and defining
bor... |
Topology\Bornology\BoundedOperation.lean | /-
Copyright (c) 2024 Kalle Kytölä. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kalle Kytölä
-/
import Mathlib.Analysis.Normed.Group.Basic
import Mathlib.Analysis.Normed.Field.Basic
/-!
# Bounded operations
This file introduces type classes for bornologically boun... |
Topology\Bornology\Constructions.lean | /-
Copyright (c) 2022 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
import Mathlib.Topology.Bornology.Basic
/-!
# Bornology structure on products and subtypes
In this file we define `Bornology` and `BoundedSpace` instances o... |
Topology\Bornology\Hom.lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Topology.Bornology.Basic
/-!
# Locally bounded maps
This file defines locally bounded maps between bornologies.
We use the `DFunLike` design, so each ty... |
Topology\Category\Born.lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.CategoryTheory.ConcreteCategory.BundledHom
import Mathlib.Topology.Bornology.Hom
/-!
# The category of bornologies
This defines `Born`, the category of b... |
Topology\Category\CompactlyGenerated.lean | /-
Copyright (c) 2024 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
import Mathlib.Topology.Compactness.CompactlyGeneratedSpace
import Mathlib.CategoryTheory.Elementwise
/-!
# Compactly generated topological spaces
This file def... |
Topology\Category\Compactum.lean | /-
Copyright (c) 2020 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz
-/
import Mathlib.CategoryTheory.Monad.Types
import Mathlib.CategoryTheory.Monad.Limits
import Mathlib.CategoryTheory.Equivalence
import Mathlib.Topology.Category.CompHaus.Basic... |
Topology\Category\FinTopCat.lean | /-
Copyright (c) 2024 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
import Mathlib.CategoryTheory.FintypeCat
import Mathlib.Topology.Category.TopCat.Basic
/-!
# Category of finite topological spaces
Definition of the category of... |
Topology\Category\Locale.lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Order.Category.Frm
/-!
# The category of locales
This file defines `Locale`, the category of locales. This is the opposite of the category of frames.
-/
... |
Topology\Category\Sequential.lean | /-
Copyright (c) 2024 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
import Mathlib.CategoryTheory.Elementwise
import Mathlib.Topology.Sequences
import Mathlib.Topology.Instances.Discrete
import Mathlib.Topology.Category.TopCat.Bas... |
Topology\Category\TopCommRingCat.lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.Algebra.Category.Ring.Basic
import Mathlib.Topology.Category.TopCat.Basic
import Mathlib.Topology.Algebra.Ring.Basic
/-!
# Category of topological com... |
Topology\Category\UniformSpace.lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton, Patrick Massot, Scott Morrison
-/
import Mathlib.CategoryTheory.Adjunction.Reflective
import Mathlib.CategoryTheory.ConcreteCategory.UnbundledHom
import Mathlib.CategoryTh... |
Topology\Category\CompHaus\Basic.lean | /-
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
-/
import Mathlib.CategoryTheory.Monad.Limits
import Mathlib.Topology.StoneCech
import Mathlib.Topology.UrysohnsLemma
import Mathlib.Topology.Category.CompHausLike... |
Topology\Category\CompHaus\EffectiveEpi.lean | /-
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
-/
import Mathlib.Topology.Category.CompHaus.Limits
import Mathlib.Topology.Category.CompHausLike.EffectiveEpi
/-!
# Effective epimorphisms in `CompHaus`
Thi... |
Topology\Category\CompHaus\Limits.lean | /-
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
-/
import Mathlib.Topology.Category.CompHaus.Basic
import Mathlib.Topology.Category.CompHausLike.Limits
/-!
# Explicit limits and colimits
This file applies ... |
Topology\Category\CompHaus\Projective.lean | /-
Copyright (c) 2021 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import Mathlib.Topology.Category.CompHaus.Basic
import Mathlib.Topology.StoneCech
import Mathlib.CategoryTheory.Preadditive.Projective
import Mathlib.CategoryTheory.C... |
Topology\Category\CompHausLike\Basic.lean | /-
Copyright (c) 2024 Dagur Asgeirsson. 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
-/
import Mathlib.CategoryTheory.Functor.ReflectsIso
import Mathlib.Topology.Category.TopCat.Basic
/-!
# Categori... |
Topology\Category\CompHausLike\EffectiveEpi.lean | /-
Copyright (c) 2024 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz, Dagur Asgeirsson
-/
import Mathlib.CategoryTheory.Sites.Coherent.Comparison
import Mathlib.Topology.Category.CompHausLike.Limits
/-!
# Effective epimorphisms in `CompHau... |
Topology\Category\CompHausLike\Limits.lean | /-
Copyright (c) 2024 Dagur Asgeirsson. 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
-/
import Mathlib.CategoryTheory.Extensive
import Mathlib.CategoryTheory.Limits.Preserves.Finite
import Mathlib.To... |
Topology\Category\LightProfinite\AsLimit.lean | /-
Copyright (c) 2024 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
import Mathlib.Topology.Category.LightProfinite.Basic
/-!
# Light profinite sets as limits of finite sets.
We show that any light profinite set is isomorphic to ... |
Topology\Category\LightProfinite\Basic.lean | /-
Copyright (c) 2023 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
import Mathlib.CategoryTheory.Limits.Shapes.Countable
import Mathlib.Topology.Category.Profinite.AsLimit
import Mathlib.Topology.Category.Profinite.CofilteredLimi... |
Topology\Category\LightProfinite\EffectiveEpi.lean | /-
Copyright (c) 2023 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
import Mathlib.Topology.Category.CompHausLike.EffectiveEpi
import Mathlib.Topology.Category.LightProfinite.Limits
/-!
# Effective epimorphisms in `LightProfinite... |
Topology\Category\LightProfinite\Limits.lean | /-
Copyright (c) 2024 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
import Mathlib.Topology.Category.CompHausLike.Limits
import Mathlib.Topology.Category.LightProfinite.Basic
/-!
# Explicit limits and colimits
This file applies ... |
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