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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
• 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