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• Open set
  ...{\delta_x}(X)\subseteq U]}} - (recall that {{M|B_r(x)}} denotes the [[open ball]] of radius {{M|r}} centred at {{M|x}}) or ** For all {{M|x}} in {{M|U}} there is an [[open ball]] centred at {{M|x}} entirely contained within {{M|U}}
  4 KB (677 words) - 02:26, 29 November 2015
• Open ball
  Given a [[metric space]] {{M|(X,d)}} the ''open ball centred at {{M|x_0\in X}} of radius {{M|r>0}}'', denoted {{M|B_r(x_0)}} (ho {{Note|1=The open ball must be proved to be open, it is not true by definition. See below}}
  4 KB (842 words) - 02:00, 29 November 2015
• Site projects:Patrolling topology/Task list
  * [[Closed set]] * [[Open and closed maps]]
  4 KB (404 words) - 21:36, 30 September 2016
• N-cell
  ===Closed {{M|n}}-cell=== ...overline{\mathbb{B}^n} }} or {{M|\overline{\mathbb{B} }^n}}, is a [[closed ball]] of radius {{M|1}} based at the origin.
  2 KB (369 words) - 19:57, 14 January 2017
• A compact and convex subset of Euclidean n-space with non-empty interior is a closed n-cell and its interior is an open n-cell/Statement
  * {{M|X}} is a [[closed n-cell|closed {{n|cell}}]] and its {{link|interior|topology}} is an [[open n-cell|open {{ ...^n} }} is the [[closed unit ball]]<ref group="Note">Recall the closed unit ball is:
  2 KB (323 words) - 20:14, 14 January 2017
• Notes:Functional Analysis II
  * [[Closed unit ball]] - we will use {{M|\overline{\mathbb{B} } }} or {{M|\overline{\mathbb{B}_X ...} centred at {{M|0}} of radius {{M|1}} - {{Caveat|easily muddled with open ball}}.
  4 KB (818 words) - 12:00, 9 February 2017
• Sphere (topological manifold)
  ...s (may) be sometimes used to denote the [[closed unit ball|''closed'' unit ball]] instead.</ref>
  2 KB (429 words) - 05:05, 12 March 2017
• Exercises:Saul - Algebraic Topology - 9/Exercise 9.7
  ...^3}} which takes an [[open neighbourhood]] of {{M|x}} onto the [[open unit ball]] at the origin. ...\crp-\{x\} }} is an [[open set]] in {{M|\crp}} - clearly the complement is closed!
  8 KB (1,299 words) - 13:33, 15 March 2017
• Simply connected topological space
  * [[The closed unit ball in R^n less the origin is a simply connected topological subspace for n gre ** Follows from [[The closed unit ball in R^n less the origin strongly deformation retracts to the (n-1) sphere|{{
  4 KB (601 words) - 16:10, 24 April 2017