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• Topology
  * [[Indiscrete topology]] ({{AKA}}: [[Trivial topology]]) - the only open sets are {{M|X}} itself and {{M|\emptyset}} If {{M|(X,d)}} is a [[metric space]], then we have the:
  3 KB (543 words) - 09:28, 30 December 2016
• Topological space
  ...s a topology, see [[Topology induced by a metric|the topology induced by a metric space]] *# [[Trivial topology]] - the topology {{M|1=\mathcal{J}=\{\emptyset, X\} }}
  2 KB (268 words) - 13:37, 20 April 2016
• Open set
  ===Metric space=== In a [[metric space]] {{M|(X,d)}} there are 2 definitions of open set, however it will be
  4 KB (677 words) - 02:26, 29 November 2015
• Norm
  * Every ''norm'' induces a [[metric]] ===Metric induced by a norm===
  6 KB (1,026 words) - 20:33, 9 April 2017
• Hausdorff space
  * Link to a theorem about all metric spaces being Hausdorff. ...he equivalent form claims - I did say "no proof will be hand-waved away as trivial" but it certainly isn't worth my time now [[User:Alec|Alec]] ([[User talk:A
  4 KB (679 words) - 22:52, 22 February 2017
• Discrete metric and topology/Metric space definition
  ...Analysis - George Bachman and Lawrence Narici</ref> is the [[Metric space|metric]] defined as follows: {{Definition|Metric Space|Topology}}
  1,004 B (160 words) - 06:08, 27 November 2015
• Borel sigma-algebra
  ...uced by a metric|topology induced by]] the [[Absolute value|absolute value metric]], {{M|\vert\cdot\vert}}). ...nerated by|generated by]] the [[Open set|open sets]] of the [[Metric space|metric space]] {{M|(\mathbb{R},\vert\cdot\vert)}}. We denote it as:
  5 KB (854 words) - 09:25, 6 August 2015
• Trivial topology
  The ''trivial topology'' (sometimes known as the ''indiscrete topology''<ref name="Top">T ...opology induced by a metric|topology induced by a metric]], the [[Discrete metric]] specifically.<br/>
  1 KB (235 words) - 16:41, 14 August 2015
• Site projects:Patrolling topology/Task list
  * [[Complete metric space]] * [[Discrete metric]]
  4 KB (404 words) - 21:36, 30 September 2016
• A subset of a topological space is open if and only if it is a neighbourhood to all of its points
  <!-- as this proof is so trivial it is possibly duplicated here ...olved if you use the metric space definitions (rather than considering the metric space as a topological space)}}
  8 KB (1,529 words) - 00:27, 6 September 2016
• Dense
  Let {{Top.|X|J}} be a [[topological space]], and {{M|(X,d)}} be a [[metric space]]. Then for an arbitrary [[subset of]] {{M|X}}, say {{M|A\in\mathcal{ # '''Metric: ''' {{M|\forall x\in X\forall\epsilon>0[B_\epsilon(x)\cap A\neq\emptyset}}
  6 KB (1,097 words) - 04:15, 1 January 2017
• Constant loop based at a point
  # [[Trivial loop]] # [[Trivial loop based at a point]]
  3 KB (479 words) - 21:03, 1 November 2016
• An open ball contains another open ball centred at each of its points
  ...pen ball containing it in the intersection]] which is a precursor to the [[metric topology]] Let {{M|(X,d)}} be a [[metric space]]. Then we claim:
  4 KB (824 words) - 17:45, 16 January 2017
• Trivial
  ...ng is trivial it means very little work needs to be done to show it holds. Trivial can also mean the argument is [[vacuous]], for example {{M|\forall x\in X[P ...he group: {{M|(\{e\},*:\{e\}\times\{e\}\rightarrow\{e\})}} is called the [[trivial group]], {{M|e}} is the identity element and {{M|e*e\eq e}} is the only ope
  1 KB (171 words) - 13:29, 16 February 2017
• Locally Euclidean topological space
  *** Recall that "''[[an open set in a metric space contains an open ball about all of its points]]''", this means: ...thbb{R}^n)}} as {{M|d(\varphi'(p),\varphi'(p)):\eq 0}} regardless of the [[metric]] used
  4 KB (667 words) - 14:32, 20 February 2017