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• A subset of a topological space is disconnected if and only if it can be covered by two non-empty-in-the-subset and disjoint-in-the-subset sets that are open in the space itself
  {{Stub page|grade=A|msg=Taking a break now, flesh out in the future}} {{Requires proof|grade=A|msg=This is actually rather important and ought to be done<br/><center><gallery>
  656 B (105 words) - 09:39, 2 October 2016
• A subset of a topological space is disconnected if and only if it can be covered by two non-empty-in-the-subset and disjoint-in-the-subset sets that are open in the space itself/Statement
  ...ological space]] and let {{M|A\in\mathcal{P}(X)}} be an arbitrary [[subset of]] {{M|X}}, then{{rITTBM}}: ...{{link|disconnected|topology}} (the very definition of {{link|disconnected subset|topology}})
  1 KB (196 words) - 09:39, 2 October 2016

Page text matches

• Connected (topology)
  {{Refactor notice|grade=A|msg=Ancient page, needs an update, linking to theorems, so forth}} ...t be put off if you have found ''another'' definition! I have started with the most intuitive definition
  5 KB (866 words) - 01:52, 1 October 2016
• Disconnected (topology)
  ...ere's not much more to be said, but it does meet the defining criteria for a stub page, hence this}} : '''Note: ''' much more information may be found on the {{link|connected|topology}} page, this page exists just to document disconn
  1 KB (153 words) - 23:59, 30 September 2016
• A subset of a topological space is disconnected if and only if it can be covered by two non-empty-in-the-subset and disjoint-in-the-subset sets that are open in the space itself
  {{Stub page|grade=A|msg=Taking a break now, flesh out in the future}} {{Requires proof|grade=A|msg=This is actually rather important and ought to be done<br/><center><gallery>
  656 B (105 words) - 09:39, 2 October 2016
• Connected (topology)/Equivalent conditions
  ...arriving here from a search page see {{link|connected|topology}} or {{link|disconnected|topology}} ==Equivalent conditions to being connected/disconnected==
  2 KB (276 words) - 00:21, 2 October 2016
• The image of a connected set is connected
  ...ty written right before bed, so needs checking. This is also "the theorem" of connectedness}} ...{{M|f:X\rightarrow Y}} be a ''[[continuous]]'' [[map]]. Then, for any {{M|A\in\mathcal{P}(X)}}, we have{{rITTBM}}:
  2 KB (422 words) - 04:10, 3 October 2016
• Notes:CW-Complex
  ...lural|CW-Complex|es}} in terms of what they are but no so much in terms of a formal definition. This page details my research. ==Munkres: Elements of Algebraic Topology==
  10 KB (1,736 words) - 01:00, 23 January 2017