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- ...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\i3 KB (543 words) - 09:28, 30 December 2016
- '''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 has1 KB (236 words) - 01:13, 6 April 2015
- ...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
- * '''Topological n-manifold''' - A [[topological space]], {{Top.|M|J}} that is: *# [[Second countable topological space]]4 KB (716 words) - 14:24, 16 May 2016
- ...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
- ...]], 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