Create the page "Finite complement topology" on this wiki! See also the search results found.

• Ultrafilter
  * For every set <math>A \subseteq X</math>, either <math>A</math> or its [[complement]] is an element of <math>\mathcal{F}</math>. ...rivial, or ''free'', or ''non-principle''. Evidently, the only filters on finite sets are trivial.
  9 KB (1,685 words) - 20:28, 13 October 2019
• Closed set
  ...ing, for example, any [[metric space]]) is closed [[if and only if]] its [[complement]] is an [[open set]], or alternatively if its [[closure]] is equal to itsel ...losed sets is a closed set. Also, the union of any two closed sets (or any finite number of closed sets) is a closed set. Note, however, that the union of an
  1 KB (232 words) - 18:33, 1 March 2010
• Separation axioms
  ...5 \subset T_6</math>. Each axiom is a strictly stronger condition upon the topology than the previous axiom. ...at is <math>T_1</math> but not <math>T_2</math> is the [[finite complement topology]] on any infinite space.
  5 KB (672 words) - 13:28, 4 June 2018