path stringlengths 11 71 | content stringlengths 75 124k |
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Topology\Category\LightProfinite\Sequence.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.Compactification.OnePoint
import Mathlib.Topology.Category.LightProfinite.Basic
/-!
# The light profinite set classifying convergent sequ... |
Topology\Category\Profinite\AsLimit.lean | /-
Copyright (c) 2021 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Calle Sönne, Adam Topaz
-/
import Mathlib.Topology.Category.Profinite.Basic
import Mathlib.Topology.DiscreteQuotient
/-!
# Profinite sets as limits of finite sets.
We show that any profi... |
Topology\Category\Profinite\Basic.lean | /-
Copyright (c) 2020 Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, Calle Sönne
-/
import Mathlib.CategoryTheory.FintypeCat
import Mathlib.Topology.Category.CompHaus.Basic
import Mathlib.Topology.LocallyConstant.Basic
/-!
# The category ... |
Topology\Category\Profinite\CofilteredLimit.lean | /-
Copyright (c) 2021 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz
-/
import Mathlib.Topology.Category.Profinite.Basic
import Mathlib.Topology.LocallyConstant.Basic
import Mathlib.Topology.DiscreteQuotient
import Mathlib.Topology.Category.TopCa... |
Topology\Category\Profinite\EffectiveEpi.lean | /-
Copyright (c) 2023 Jon Eugster. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson, Boris Bolvig Kjær, Jon Eugster, Sina Hazratpour
-/
import Mathlib.CategoryTheory.Sites.Coherent.ReflectsPreregular
import Mathlib.Topology.Category.CompHaus.EffectiveEpi... |
Topology\Category\Profinite\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.Profinite.Basic
import Mathlib.Topology.Category.CompHausLike.Limits
/-!
# Explicit limits and colimits
This file applies... |
Topology\Category\Profinite\Nobeling.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.Algebra.Category.ModuleCat.Free
import Mathlib.Topology.Category.Profinite.CofilteredLimit
import Mathlib.Topology.Category.Profinite.Product
impor... |
Topology\Category\Profinite\Product.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.Profinite.Basic
/-!
# Compact subsets of products as limits in `Profinite`
This file exhibits a compact subset `C` of a product... |
Topology\Category\Profinite\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.Profinite.Basic
import Mathlib.Topology.StoneCech
import Mathlib.CategoryTheory.Preadditive.Projective
import Mathlib.CategoryTheory.... |
Topology\Category\Stonean\Adjunctions.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.Stonean.Basic
import Mathlib.Topology.Category.TopCat.Adjunctions
import Mathlib.Topology.StoneCech
/-!
# Adjunctions involving ... |
Topology\Category\Stonean\Basic.lean | /-
Copyright (c) 2023 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz
-/
import Mathlib.Topology.ExtremallyDisconnected
import Mathlib.Topology.Category.CompHaus.Projective
import Mathlib.Topology.Category.Profinite.Basic
/-!
# Extremally disconne... |
Topology\Category\Stonean\EffectiveEpi.lean | /-
Copyright (c) 2023 Jon Eugster. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson, Boris Bolvig Kjær, Jon Eugster, Sina Hazratpour, Nima Rasekh
-/
import Mathlib.CategoryTheory.Sites.Coherent.ReflectsPreregular
import Mathlib.Topology.Category.CompHaus... |
Topology\Category\Stonean\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, Filippo A. E. Nuccio, Riccardo Brasca
-/
import Mathlib.Topology.Category.CompHausLike.Limits
import Mathlib.Topology.Category.Stonean.Basic
/-!
# Explicit l... |
Topology\Category\TopCat\Adjunctions.lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Mario Carneiro
-/
import Mathlib.Topology.Category.TopCat.Basic
import Mathlib.CategoryTheory.Adjunction.Basic
/-!
# Adjunctions regarding the category of topological ... |
Topology\Category\TopCat\Basic.lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Scott Morrison, Mario Carneiro
-/
import Mathlib.CategoryTheory.ConcreteCategory.BundledHom
import Mathlib.Topology.ContinuousFunction.Basic
/-!
# Category instance fo... |
Topology\Category\TopCat\EffectiveEpi.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.EffectiveEpi.RegularEpi
import Mathlib.CategoryTheory.EffectiveEpi.Comp
import Mathlib.Topology.Category.TopCat.Limits.Pullbacks
/-!... |
Topology\Category\TopCat\EpiMono.lean | /-
Copyright (c) 2019 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton
-/
import Mathlib.Topology.Category.TopCat.Adjunctions
import Mathlib.CategoryTheory.Functor.EpiMono
/-!
# Epi- and monomorphisms in `Top`
This file shows that a continuous ... |
Topology\Category\TopCat\OpenNhds.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.Topology.Category.TopCat.Opens
import Mathlib.Data.Set.Subsingleton
/-!
# The category of open neighborhoods of a point
Given an object `X` of the ca... |
Topology\Category\TopCat\Opens.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.CategoryTheory.Category.Preorder
import Mathlib.CategoryTheory.EqToHom
import Mathlib.Topology.Category.TopCat.EpiMono
import Mathlib.Topology.Sets.Ope... |
Topology\Category\TopCat\Yoneda.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.Preserves.Finite
import Mathlib.CategoryTheory.Limits.Opposites
import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Product... |
Topology\Category\TopCat\Limits\Basic.lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Scott Morrison, Mario Carneiro, Andrew Yang
-/
import Mathlib.Topology.Category.TopCat.Basic
import Mathlib.CategoryTheory.Limits.Types
import Mathlib.CategoryTheory.Li... |
Topology\Category\TopCat\Limits\Cofiltered.lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Scott Morrison, Mario Carneiro, Andrew Yang
-/
import Mathlib.Topology.Category.TopCat.Limits.Basic
import Mathlib.CategoryTheory.Filtered.Basic
/-!
# Cofiltered limit... |
Topology\Category\TopCat\Limits\Konig.lean | /-
Copyright (c) 2021 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller
-/
import Mathlib.CategoryTheory.Filtered.Basic
import Mathlib.Topology.Category.TopCat.Limits.Basic
/-!
# Topological Kőnig's lemma
A topological version of Kőnig's lemma i... |
Topology\Category\TopCat\Limits\Products.lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Scott Morrison, Mario Carneiro, Andrew Yang
-/
import Mathlib.Topology.Category.TopCat.EpiMono
import Mathlib.Topology.Category.TopCat.Limits.Basic
import Mathlib.Categ... |
Topology\Category\TopCat\Limits\Pullbacks.lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Scott Morrison, Mario Carneiro, Andrew Yang
-/
import Mathlib.Topology.Category.TopCat.Limits.Products
/-!
# Pullbacks and pushouts in the category of topological spac... |
Topology\Compactification\OnePoint.lean | /-
Copyright (c) 2021 Yourong Zang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yourong Zang, Yury Kudryashov
-/
import Mathlib.Data.Fintype.Option
import Mathlib.Topology.Separation
import Mathlib.Topology.Sets.Opens
/-!
# The OnePoint Compactification
We constru... |
Topology\Compactness\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, Yury Kudryashov
-/
import Mathlib.Order.Filter.Basic
import Mathlib.Topology.Bases
import Mathlib.Data.Set.Accumulate
import Mathlib.Topology.Bornology.... |
Topology\Compactness\CompactlyGeneratedSpace.lean | /-
Copyright (c) 2024 Etienne Marion. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson, Etienne Marion
-/
import Mathlib.Topology.Category.CompHaus.Basic
import Mathlib.Topology.Compactification.OnePoint
/-!
# Compactly generated topological spaces
Thi... |
Topology\Compactness\Lindelof.lean | /-
Copyright (c) 2023 Josha Dekker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Josha Dekker
-/
import Mathlib.Topology.Bases
import Mathlib.Order.Filter.CountableInter
import Mathlib.Topology.Compactness.SigmaCompact
/-!
# Lindelöf sets and Lindelöf spaces
## Mai... |
Topology\Compactness\LocallyCompact.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
-/
import Mathlib.Topology.Compactness.Compact
/-!
# Locally compact spaces
We define the following classes of topological spaces:
* `W... |
Topology\Compactness\Paracompact.lean | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton, Yury Kudryashov
-/
import Mathlib.Topology.Homeomorph
import Mathlib.Data.Option.Basic
/-!
# Paracompact topological spaces
A topological space `X` is said to be paraco... |
Topology\Compactness\PseudometrizableLindelof.lean | /-
Copyright (c) 2023 Josha Dekker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Josha Dekker
-/
import Mathlib.Topology.Metrizable.Basic
import Mathlib.Topology.Compactness.Lindelof
/-!
# Second-countability of pseudometrizable Lindelöf spaces
Factored out from `... |
Topology\Compactness\SigmaCompact.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
-/
import Mathlib.Topology.Compactness.LocallyCompact
/-!
# Sigma-compactness in topological spaces
## Main definitions
* `IsSigmaCompa... |
Topology\Connected\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, Yury Kudryashov
-/
import Mathlib.Data.Set.Basic
import Mathlib.Order.SuccPred.Relation
import Mathlib.Topology.Irreducible
/-!
# Connected subsets of ... |
Topology\Connected\Clopen.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
-/
import Mathlib.Data.Set.Subset
import Mathlib.Topology.Clopen
import Mathlib.Topology.Connected.Basic
/-!
# Connected subsets and th... |
Topology\Connected\LocallyConnected.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.Connected.Basic
/-!
# Locally connected topological spaces
A topological space is **locally connected** if each neighborhood filter admi... |
Topology\Connected\PathConnected.lean | /-
Copyright (c) 2020 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot
-/
import Mathlib.Topology.Order.ProjIcc
import Mathlib.Topology.CompactOpen
import Mathlib.Topology.UnitInterval
/-!
# Path connectedness
## Main definitions
In the ... |
Topology\Connected\Separation.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.Separation
/-!
# Separation and (dis)connectedness properties of topological spaces.
This file provides an instance `T2Space X` given `T... |
Topology\Connected\TotallyDisconnected.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Patrick Massot, Yury Kudryashov
-/
import Mathlib.Topology.Connected.Clopen
/-!
# Totally disconnected and totally separated topological spaces
## Main definitions
We define th... |
Topology\ContinuousFunction\Algebra.lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Nicolò Cavalleri
-/
import Mathlib.Algebra.Algebra.Pi
import Mathlib.Algebra.Order.Group.Lattice
import Mathlib.Algebra.Periodic
import Mathlib.Algebra.Algebra.Subalgeb... |
Topology\ContinuousFunction\Basic.lean | /-
Copyright (c) 2020 Nicolò Cavalleri. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nicolò Cavalleri
-/
import Mathlib.Data.Set.UnionLift
import Mathlib.Topology.Homeomorph
/-!
# Continuous bundled maps
In this file we define the type `ContinuousMap` of continuous... |
Topology\ContinuousFunction\Bounded.lean | /-
Copyright (c) 2018 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Mario Carneiro, Yury Kudryashov, Heather Macbeth
-/
import Mathlib.Algebra.Module.MinimalAxioms
import Mathlib.Topology.ContinuousFunction.Algebra
import Mathlib.... |
Topology\ContinuousFunction\CocompactMap.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.Topology.ContinuousFunction.Basic
/-!
# Cocompact continuous maps
The type of *cocompact continuous maps* are those which tend to the cocompact filter ... |
Topology\ContinuousFunction\Compact.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.Topology.ContinuousFunction.Bounded
import Mathlib.Topology.UniformSpace.Compact
import Mathlib.Topology.CompactOpen
import Mathlib.Topology.Sets.Compa... |
Topology\ContinuousFunction\CompactlySupported.lean | /-
Copyright (c) 2024 Yoh Tanimoto. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yoh Tanimoto
-/
import Mathlib.Topology.ContinuousFunction.CocompactMap
import Mathlib.Topology.ContinuousFunction.ZeroAtInfty
import Mathlib.Topology.Support
/-!
# Compactly supported ... |
Topology\ContinuousFunction\ContinuousMapZero.lean | /-
Copyright (c) 2024 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import Mathlib.Topology.ContinuousFunction.Algebra
/-!
# Continuous maps sending zero to zero
This is the type of continuous maps from `X` to `R` such that `(0 : X) ↦... |
Topology\ContinuousFunction\Ideals.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.Topology.Algebra.Algebra
import Mathlib.Topology.ContinuousFunction.Compact
import Mathlib.Topology.UrysohnsLemma
import Mathlib.Analysis.RCLike.Basic
im... |
Topology\ContinuousFunction\LocallyConstant.lean | /-
Copyright (c) 2021 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import Mathlib.Topology.LocallyConstant.Algebra
import Mathlib.Topology.ContinuousFunction.Basic
import Mathlib.Topology.ContinuousFunction.Algebra
/-!
# The algebra morph... |
Topology\ContinuousFunction\Ordered.lean | /-
Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Shing Tak Lam
-/
import Mathlib.Topology.ContinuousFunction.Basic
import Mathlib.Topology.Order.Lattice
import Mathlib.Topology.Order.ProjIcc
/-!
# Bundled continuous ... |
Topology\ContinuousFunction\Polynomial.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.Topology.Algebra.Polynomial
import Mathlib.Topology.ContinuousFunction.Algebra
import Mathlib.Topology.UnitInterval
import Mathlib.Algebra.Star.Subalge... |
Topology\ContinuousFunction\Sigma.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.CompactOpen
/-!
# Equivalence between `C(X, Σ i, Y i)` and `Σ i, C(X, Y i)`
If `X` is a connected topological space, then for every contin... |
Topology\ContinuousFunction\StarOrdered.lean | /-
Copyright (c) 2024 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import Mathlib.Analysis.Complex.Basic
import Mathlib.Data.Real.StarOrdered
import Mathlib.Topology.ContinuousFunction.Algebra
import Mathlib.Topology.ContinuousFunction... |
Topology\ContinuousFunction\StoneWeierstrass.lean | /-
Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Heather Macbeth
-/
import Mathlib.Algebra.Algebra.Subalgebra.Unitization
import Mathlib.Analysis.RCLike.Basic
import Mathlib.Topology.Algebra.StarSubalgebra
import Math... |
Topology\ContinuousFunction\T0Sierpinski.lean | /-
Copyright (c) 2022 Ivan Sadofschi Costa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ivan Sadofschi Costa
-/
import Mathlib.Topology.Order
import Mathlib.Topology.Sets.Opens
import Mathlib.Topology.ContinuousFunction.Basic
/-!
# Any T0 space embeds in a product ... |
Topology\ContinuousFunction\Units.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.Analysis.Normed.Ring.Units
import Mathlib.Algebra.Algebra.Spectrum
import Mathlib.Topology.ContinuousFunction.Algebra
/-!
# Units of continuous function... |
Topology\ContinuousFunction\Weierstrass.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.Analysis.SpecialFunctions.Bernstein
import Mathlib.Topology.Algebra.Algebra
/-!
# The Weierstrass approximation theorem for continuous functions on `[... |
Topology\ContinuousFunction\ZeroAtInfty.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.Topology.ContinuousFunction.Bounded
import Mathlib.Topology.ContinuousFunction.CocompactMap
/-!
# Continuous functions vanishing at infinity
The type o... |
Topology\Defs\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, Jeremy Avigad
-/
import Mathlib.Order.SetNotation
import Mathlib.Tactic.Continuity
import Mathlib.Tactic.FunProp
/-!
# Basic definitions about topologic... |
Topology\Defs\Filter.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, Jeremy Avigad
-/
import Mathlib.Topology.Defs.Basic
import Mathlib.Order.Filter.Ultrafilter
import Mathlib.Data.Set.Lattice
/-!
# Definitions about fil... |
Topology\Defs\Induced.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, Jeremy Avigad
-/
import Mathlib.Topology.Basic
/-!
# Induced and coinduced topologies
In this file we define the induced and coinduced topologies,
as w... |
Topology\Defs\Sequences.lean | /-
Copyright (c) 2018 Jan-David Salchow. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jan-David Salchow, Patrick Massot, Yury Kudryashov
-/
import Mathlib.Topology.Defs.Filter
/-!
# Sequences in topological spaces
In this file we define sequential closure, continui... |
Topology\EMetricSpace\Basic.lean | /-
Copyright (c) 2015, 2017 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Robert Y. Lewis, Johannes Hölzl, Mario Carneiro, Sébastien Gouëzel
-/
import Mathlib.Data.ENNReal.Real
import Mathlib.Order.Interval.Finset.Nat
import Mathlib.Topol... |
Topology\EMetricSpace\Lipschitz.lean | /-
Copyright (c) 2018 Rohan Mitta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rohan Mitta, Kevin Buzzard, Alistair Tucker, Johannes Hölzl, Yury Kudryashov
-/
import Mathlib.Logic.Function.Iterate
import Mathlib.Topology.EMetricSpace.Basic
import Mathlib.Tactic.GCon... |
Topology\EMetricSpace\Paracompact.lean | /-
Copyright (c) 202 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
import Mathlib.SetTheory.Ordinal.Basic
import Mathlib.Tactic.GCongr
import Mathlib.Topology.EMetricSpace.Basic
import Mathlib.Topology.Compactness.Paracompact
... |
Topology\FiberBundle\Basic.lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Floris van Doorn, Heather Macbeth
-/
import Mathlib.Topology.FiberBundle.Trivialization
import Mathlib.Topology.Order.LeftRightNhds
/-!
# Fiber bundles
Mathemat... |
Topology\FiberBundle\Constructions.lean | /-
Copyright (c) 2022 Nicolò Cavalleri. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nicolò Cavalleri, Sébastien Gouëzel, Heather Macbeth, Floris van Doorn
-/
import Mathlib.Topology.FiberBundle.Basic
/-!
# Standard constructions on fiber bundles
This file contains... |
Topology\FiberBundle\IsHomeomorphicTrivialBundle.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.Homeomorph
/-!
# Maps equivariantly-homeomorphic to projection in a product
This file contains the definition `IsHomeomorphicTrivialFi... |
Topology\FiberBundle\Trivialization.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.Data.Bundle
import Mathlib.Data.Set.Image
import Mathlib.Topology.PartialHomeomorph
import Mathlib.Topology.Order.Basic
/-!
# Trivializations
#... |
Topology\Hom\Open.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.ContinuousFunction.Basic
/-!
# Continuous open maps
This file defines bundled continuous open maps.
We use the `DFunLike` design, so each type ... |
Topology\Homotopy\Basic.lean | /-
Copyright (c) 2021 Shing Tak Lam. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Shing Tak Lam
-/
import Mathlib.Topology.Order.ProjIcc
import Mathlib.Topology.ContinuousFunction.Ordered
import Mathlib.Topology.CompactOpen
import Mathlib.Topology.UnitInterval
/-!
#... |
Topology\Homotopy\Contractible.lean | /-
Copyright (c) 2022 Praneeth Kolichala. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Praneeth Kolichala
-/
import Mathlib.Topology.Homotopy.Path
import Mathlib.Topology.Homotopy.Equiv
/-!
# Contractible spaces
In this file, we define `ContractibleSpace`, a space ... |
Topology\Homotopy\Equiv.lean | /-
Copyright (c) 2021 Shing Tak Lam. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Shing Tak Lam
-/
import Mathlib.Topology.Homotopy.Basic
/-!
# Homotopy equivalences between topological spaces
In this file, we define homotopy equivalences between topological space... |
Topology\Homotopy\HomotopyGroup.lean | /-
Copyright (c) 2021 Roberto Alvarez. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Roberto Alvarez
-/
import Mathlib.AlgebraicTopology.FundamentalGroupoid.FundamentalGroup
import Mathlib.GroupTheory.EckmannHilton
import Mathlib.Logic.Equiv.TransferInstance
import Ma... |
Topology\Homotopy\HSpaces.lean | /-
Copyright (c) 2022 Filippo A. E. Nuccio Mortarino Majno di Capriglio. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Filippo A. E. Nuccio, Junyan Xu
-/
import Mathlib.Topology.CompactOpen
import Mathlib.Topology.Connected.PathConnected
import Mathlib.Topology.Homoto... |
Topology\Homotopy\Path.lean | /-
Copyright (c) 2021 Shing Tak Lam. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Shing Tak Lam
-/
import Mathlib.Topology.Homotopy.Basic
import Mathlib.Topology.Connected.PathConnected
import Mathlib.Analysis.Convex.Basic
/-!
# Homotopy between paths
In this file,... |
Topology\Homotopy\Product.lean | /-
Copyright (c) 2021 Praneeth Kolichala. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Praneeth Kolichala
-/
import Mathlib.Topology.Constructions
import Mathlib.Topology.Homotopy.Path
/-!
# Product of homotopies
In this file, we introduce definitions for the produ... |
Topology\Instances\AddCircle.lean | /-
Copyright (c) 2022 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import Mathlib.Algebra.Order.ToIntervalMod
import Mathlib.Algebra.Ring.AddAut
import Mathlib.Data.Nat.Totient
import Mathlib.GroupTheory.Divisible
import Mathlib.Topology.C... |
Topology\Instances\CantorSet.lean | /-
Copyright (c) 2024 Jana Göken. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Artur Szafarczyk, Suraj Krishna M S, Jean-Baptiste Stiegler, Isabelle Dubois,
Tomáš Jakl, Lorenzo Zanichelli, Alina Yan, Emilie Uthaiwat, Jana Göken,
Filippo A. E. Nuccio
-/
import Mathlib... |
Topology\Instances\Complex.lean | /-
Copyright (c) 2022 Xavier Roblot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Xavier Roblot
-/
import Mathlib.Analysis.Complex.Basic
import Mathlib.Data.Complex.FiniteDimensional
import Mathlib.FieldTheory.IntermediateField
import Mathlib.LinearAlgebra.FiniteDime... |
Topology\Instances\Discrete.lean | /-
Copyright (c) 2022 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
import Mathlib.Order.SuccPred.Basic
import Mathlib.Topology.Order.Basic
import Mathlib.Topology.Metrizable.Uniformity
/-!
# Instances related to the discrete topology
W... |
Topology\Instances\ENNReal.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.Order.MonotoneContinuity
import Mathlib.Topology.Algebra.Order.LiminfLimsup
import Mathlib.Topology.Instances.NNReal
import Mathlib.Topology.E... |
Topology\Instances\EReal.lean | /-
Copyright (c) 2021 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.Data.Rat.Encodable
import Mathlib.Data.Real.EReal
import Mathlib.Topology.Instances.ENNReal
import Mathlib.Topology.Order.MonotoneContinuity
/-!... |
Topology\Instances\Int.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.Data.Int.Interval
import Mathlib.Data.Int.SuccPred
import Mathlib.Data.Int.ConditionallyCompleteOrder
import Mathlib.Topology.Instances... |
Topology\Instances\Irrational.lean | /-
Copyright (c) 2021 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
import Mathlib.Data.Real.Irrational
import Mathlib.Data.Rat.Encodable
import Mathlib.Topology.GDelta
/-!
# Topology of irrational numbers
In this file we pr... |
Topology\Instances\Matrix.lean | /-
Copyright (c) 2021 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash, Eric Wieser
-/
import Mathlib.Topology.Algebra.InfiniteSum.Basic
import Mathlib.Topology.Algebra.Ring.Basic
import Mathlib.Topology.Algebra.Star
import Mathlib.LinearAlgebra.... |
Topology\Instances\Nat.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.Topology.Instances.Int
/-!
# Topology on the natural numbers
The structure of a metric space on `ℕ` is introduced in this file, induc... |
Topology\Instances\NNReal.lean | /-
Copyright (c) 2018 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import Mathlib.Data.NNReal.Star
import Mathlib.Topology.Algebra.InfiniteSum.Order
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.Topology.Instances.R... |
Topology\Instances\PNat.lean | /-
Copyright (c) 2024 Miyahara Kō. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Miyahara Kō
-/
import Mathlib.Topology.Instances.Nat
/-!
# Topology on the positive natural numbers
The structure of a metric space on `ℕ+` is introduced in this file, induced from `ℝ`.... |
Topology\Instances\Rat.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.Topology.Algebra.Order.Archimedean
import Mathlib.Topology.Instances.Nat
import Mathlib.Topology.Instances.Real
/-!
# Topology on the ... |
Topology\Instances\RatLemmas.lean | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Topology.Instances.Irrational
import Mathlib.Topology.Instances.Rat
import Mathlib.Topology.Compactification.OnePoint
/-!
# Additional lemmas about ... |
Topology\Instances\Real.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.Data.Real.Star
import Mathlib.Algebra.Algebra.Basic
import Mathlib.Algebra.Periodic
import Mathlib.Topology.Algebra.Order.Field
import ... |
Topology\Instances\RealVectorSpace.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.Module.Basic
import Mathlib.Topology.Instances.Rat
import Mathlib.Algebra.Module.Rat
/-!
# Continuous additive maps are `ℝ`-linear
... |
Topology\Instances\Sign.lean | /-
Copyright (c) 2022 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
import Mathlib.Data.Sign
import Mathlib.Topology.Order.Basic
/-!
# Topology on `SignType`
This file gives `SignType` the discrete topology, and proves continuity result... |
Topology\Instances\TrivSqZeroExt.lean | /-
Copyright (c) 2023 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Algebra.TrivSqZeroExt
import Mathlib.Topology.Algebra.InfiniteSum.Basic
import Mathlib.Topology.Algebra.Module.Basic
/-!
# Topology on `TrivSqZeroExt R M`
... |
Topology\Instances\ZMod.lean | /-
Copyright (c) 2024 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
import Mathlib.Topology.Order
import Mathlib.Data.ZMod.Defs
/-!
# Topology on `ZMod N`
We equip `ZMod N` with the discrete topology.
-/
namespace ZMod
variable {N... |
Topology\LocallyConstant\Algebra.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.Algebra.Algebra.Pi
import Mathlib.LinearAlgebra.Pi
import Mathlib.Topology.LocallyConstant.Basic
/-!
# Algebraic structure on locally constant functio... |
Topology\LocallyConstant\Basic.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.Algebra.GroupWithZero.Indicator
import Mathlib.Tactic.FinCases
import Mathlib.Topology.Sets.Closeds
/-!
# Locally constant functions
This file sets u... |
Topology\Maps\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.Topology.Order
/-!
# Specific classes of maps between topological spaces
This file introduces the following propertie... |
Topology\Maps\Proper\Basic.lean | /-
Copyright (c) 2023 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker, Etienne Marion
-/
import Mathlib.Topology.Homeomorph
import Mathlib.Topology.Filter
import Mathlib.Topology.Defs.Sequences
/-!
# Proper maps between topological sp... |
Topology\Maps\Proper\UniversallyClosed.lean | /-
Copyright (c) 2023 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker, Etienne Marion
-/
import Mathlib.Topology.Maps.Proper.Basic
import Mathlib.Topology.StoneCech
/-!
# A map is proper iff it is continuous and universally closed
-/
... |
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