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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 ...