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• R^n is a topological vector space
  {{DISPLAYTITLE:{{M|\mathbb{R}^n}} is a topological vector space}} ...]'' (considered with its usual topology) [[R^n|{{M|\mathbb{R}^n}}]] is a [[topological vector space]]{{rALASR}}.
  805 B (129 words) - 14:25, 16 August 2016
• Locally Euclidean topological space of dimension n
  {{DISPLAYTITLE:Locally Euclidean topological space of dimension {{N}}}} : {{Caveat|I think this {{M|n}} might have to be unique}} as later (see [[topological manifold]]) we'll talk about the "well-defined-ness" of {{M|n}}!<ref group=
  2 KB (393 words) - 12:40, 21 February 2017

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• Topology
  ...y, usually when talk of topologies we don't mean a topology but rather a [[topological space]] which is a topology with its underlying set. See that page for more A [[topological space]] is simply a [[tuple]] consisting of a set (say {{M|X}}) and a topol
  3 KB (543 words) - 09:28, 30 December 2016
• Open set
  ===Topological space=== In a [[topological space]] {{M|(X,\mathcal{J})}} we have:
  4 KB (677 words) - 02:26, 29 November 2015
• Metric space
  ...see the relationships between metric spaces and others see: [[Subtypes of topological spaces]] * [[Topological space]]
  2 KB (336 words) - 06:07, 27 November 2015
• Continuous map
  Given two [[topological space|topological spaces]] {{M|(X,\mathcal{J})}} and {{M|(Y,\mathcal{K})}} we say that a [[ma Again, given two [[topological space|topological spaces]] {{M|(X,\mathcal{J})}} and {{M|(Y,\mathcal{K})}}, and a point {{M|x
  6 KB (972 words) - 01:44, 14 October 2016
• Closed set
  A closed set in a [[Topological space|topological space]] <math>(X,\mathcal{J})</math> is a set <math>A</math> where <math>X- * '''Note: ''' as every [[metric space]] is also a [[topological space]] it is still true that a set is closed if its complement is open.
  1 KB (238 words) - 15:36, 24 November 2015
• Product topology
  {{Requires references|grade=A|msg=Check Munkres and Topological Manifolds}} ...itrary family of [[topological spaces]]. The ''product topology'' is a new topological space defined on the [[set]] {{M|1=\prod_{\alpha\in I}X_\alpha}} (herein we
  5 KB (871 words) - 20:32, 23 September 2016
• Norm
  ==Relation to various [[subtypes of topological spaces]]== (See [[Subtypes of topological spaces]] for more information, this relationship is very important in [[Fun
  6 KB (1,026 words) - 20:33, 9 April 2017
• Sequential compactness
  Sequential compactness extends this notion to general topological spaces. A [[Topological space|topological space]] {{M|(X,\mathcal{J})}} is sequentially compact if every (infinite) [
  1 KB (228 words) - 15:37, 24 November 2015
• Measurable map
  ...e [[Borel sigma-algebra|Borel {{sigma|algebra}}]] of a [[Topological space|topological space]], {{M|(X,\mathcal{J})}}, then the {{M|\mathcal{B}((X,\mathcal{J}))}}
  5 KB (792 words) - 02:31, 3 August 2015
• Manifolds
  * [[Topological manifold]]
  2 KB (276 words) - 05:59, 7 April 2015
• Topological manifold
  '''Note:''' This page refers to a '''Topological Manifold''' a special kind of [[Manifold]] We say {{M|M}} is a ''topological manifold of dimension {{M|n}}'' or simply ''an {{M|n-}}manifold'' if it has
  1 KB (236 words) - 01:13, 6 April 2015
• Chart
  A coordinate chart - or just chart on a [[Topological manifold|topological manifold]] of dimension {{M|n}} is a pair {{M|(U,\varphi)}}<ref>John M Lee
  2 KB (322 words) - 06:32, 7 April 2015
• Transition map
  Given two [[Chart|charts]] {{M|(U,\varphi)}} and {{M|(V,\psi)}} on a topological {{M|n-}}manifold where {{M|U\cap V\ne\emptyset}}<ref>Introduction to smooth [[File:Transition map.JPG|thumb|Transition map {{M|\psi\circ\varphi}} on a topological {{n|manifold}} {{M|M}}]]
  1,003 B (156 words) - 06:33, 7 April 2015
• Atlas
  '''Note:''' this page defines an atlas on a [[Topological manifold]] which isn't very useful by itself, see [[Smooth atlas]] ...hn M Lee - Second Edition</ref> (where {{M|M}} is a [[Topological manifold|topological {{n|manifold}}]]) is a collection of [[Chart|charts]] whose domains cover {
  562 B (82 words) - 06:44, 7 April 2015
• Smooth manifold
  ...ef> a pair {{M|(M,\mathcal{A})}} where {{M|M}} is a [[Topological manifold|topological {{n|manifold}}]] and {{M|\mathcal{A} }} is a [[Smooth structure|smooth stru * A [[Topological manifold|topological manifold]] may have many different potential [[Smooth structure|smooth stru
  3 KB (413 words) - 21:09, 12 April 2015
• Sphere
  This article looks at {{M|\mathbb{S}^n}} - the sphere as a manifold or a topological space - NOT as something with a tangent plane or defined by the set of poin
  403 B (61 words) - 18:10, 16 April 2015
• Hausdorff space
  Given a [[topological space]] {{M|(X,\mathcal{J})}} we say it is ''Hausdorff''{{rITTBM}} or ''sat A topological space satisfying this property is said to be a ''Hausdorff space''{{rITTMJM
  4 KB (679 words) - 22:52, 22 February 2017
• Limit
  ...N}\exists U\in\mathcal{J}[a\in U\wedge(n> N \implies a_n\in U)]</math> - [[Topological space]] {{M|(X,\mathcal{J})}}
  2 KB (310 words) - 18:23, 8 January 2016
• Notes:Just what is in a generated sigma-algebra
  Consider a [[Topological space|topology]] on {{M|X}}, call it {{M|\mathcal{J} }}, what can we say ab
  1 KB (256 words) - 13:29, 17 June 2015
• Bounded set
  * [[Topological property theorems]]
  2 KB (409 words) - 23:31, 29 October 2016