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• Topology
  ...hen 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 detai ...l{J} }} is ''any'' collection of elements of {{M|\mathcal{J} }} (finite, [[countable]], [[uncountable]] or otherwise) then {{M|1=\bigcup_{\alpha\in I}U_\alpha\i
  3 KB (543 words) - 09:28, 30 December 2016
• Topological manifold
  '''Note:''' This page refers to a '''Topological Manifold''' a special kind of [[Manifold]] ...e following properties<ref>John M Lee - Introduction to smooth manifolds - Second Edition</ref>:
  1 KB (236 words) - 01:13, 6 April 2015
• User talk:Boris
  ...quential'' continuity is far not the (usual) continuity (since the product space is not metrizable). ...wer users are, first, probability theory and geometric measure theory, and second, functional analysis and descriptive set theory.
  13 KB (2,226 words) - 18:39, 8 April 2016
• Topological separation axioms
  ...pology]] we may derive some interesting properties that are not true for [[topological spaces]] in general. [[Cardinality]] arguments are "weak" in the sense of t ...is is what I mean by cardinality arguments are weak. They don't govern the space.
  4 KB (569 words) - 00:08, 4 May 2016
• Notes:Differential (manifolds)
  * '''Topological n-manifold''' - A [[topological space]], {{Top.|M|J}} that is: *# [[Second countable topological space]]
  4 KB (716 words) - 14:24, 16 May 2016
• Sphere (topological manifold)
  ...t}} is the [[Euclidean norm]] on [[Euclidean n-space|Euclidean {{M|(n+1)}}-space]] We claim that {{M|\mathbb{S}^n}} is a [[topological manifold]] with the following standard {{M|2n+2}} [[charts]]{{rITSMJML}}:
  2 KB (429 words) - 05:05, 12 March 2017
• Graph (topological manifold)
  ...]], with {{M|\mathbb{R}^n}} denoting [[Euclidean n-space|Euclidean {{m|n}}-space]]. Let {{M|f:U\rightarrow\mathbb{R}^k}} be a [[continuous map]] and recall ...is a [[topological n-manifold|topological {{n|manifold}}]] (literally a [[topological manifold]] of dimension {{M|n}})
  2 KB (369 words) - 12:53, 17 March 2017