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• Closed set
  2 KB (338 words) - 15:26, 6 January 2009
• Closed set/Definition
  150 bytes (21 words) - 19:23, 30 September 2009
• Closed set/Approval
  12 bytes (1 word) - 06:07, 26 September 2007
• Closed set/Related Articles
  307 bytes (43 words) - 08:34, 2 March 2024

Page text matches

• Open set/Related Articles
  [[Closed set]]
  57 bytes (6 words) - 19:17, 24 March 2008
• Door space
  ...a [[topological space]] in which each [[subset]] is [[open set|open]] or [[closed set|closed]] or both.
  623 bytes (95 words) - 00:59, 19 February 2009
• Noetherian space
  ...a [[topological space]] satisfying the [[descending chain condition]] on [[closed set]]s. A closed set in a Noetherian space is again Noetherian with respect to the [[induced top
  574 bytes (88 words) - 17:18, 7 February 2009
• Closure (topology)
  ...h>. Other equivalent definitions of the closure of A are as the smallest [[closed set]] in ''X'' containing ''A'', or the intersection of all closed sets in ''X' * The closure of a closed set ''F'' is just ''F'' itself, <math>F = \overline{F}</math>.
  1 KB (184 words) - 15:20, 6 January 2009
• Heine–Borel theorem
  ...c. As a [[topological space]], a subset is compact if and only if it is [[closed set|closed]] and [[bounded set|bounded]]. ...e]], the same statement holds: a subset is compact if and only if it is [[closed set|closed]] and [[bounded set|bounded]].
  2 KB (381 words) - 08:54, 29 December 2008
• G-delta set
  ...]]s. An '''F_σ''' space is similarly a countable [[union]] of [[closed set]]s. A '''G_δ space''' is a topological space in which every closed set is a G_δ set. A [[normal space]] which is also a G_δ
  1 KB (223 words) - 13:16, 8 March 2009
• Sober space
  ...e set|irreducible]] [[closed set]] has a unique [[generic point]]. Here a closed set is ''irreducible'' if it is not the union of two non-empty proper closed su ...open set]]s. An open set in a sober space is again a sober space, as is a closed set.
  1 KB (203 words) - 13:09, 7 February 2009
• Sober space/Definition
  A topological space in which every irreducible closed set has a unique generic point.
  121 bytes (17 words) - 12:25, 31 December 2008
• Compact space/Related Articles
  {{r|Closed set}}
  531 bytes (72 words) - 14:37, 31 October 2008
• Denseness/Related Articles
  {{r|Closed set}}
  332 bytes (44 words) - 08:34, 2 March 2024
• Cocountable topology
  ...et theory)|complement]], together with the empty set. Equivalently, the [[closed set]]s are the countable sets, together with the whole space.
  1,004 bytes (134 words) - 22:48, 17 February 2009
• Separation axioms
  * '''T3''' if a closed set ''A'' and a point ''x'' not in ''A'' have disjoint neighbourhoods * '''T3½''' if for any closed set ''A'' and point ''x'' not in ''A'' there is a Urysohn function for ''A'' an
  3 KB (430 words) - 15:28, 6 January 2009
• Cofinite topology
  ...et theory)|complement]], together with the empty set. Equivalently, the [[closed set]]s are the finite sets, together with the whole space.
  1,007 bytes (137 words) - 22:52, 17 February 2009
• Compact space
  Just as the topology on a topological space may be defined in terms of the [[closed set]]s rather than the [[open set]]s, so we may transpose the definition of com * A [[closed set]] in a compact space is again compact.
  4 KB (652 words) - 14:44, 30 December 2008
• Closure operator
  The principal example of a topological closure system is the family of [[closed set]]s in a [[topological space]]. The corresponding [[closure (topology)|clos
  2 KB (414 words) - 03:00, 14 February 2010
• Limit point
  * A subset ''S'' is [[closed set|closed]] if and only if it contains all its limit points.
  2 KB (385 words) - 22:53, 17 February 2009
• Bounded set
  ...''R'''^''n'' is [[compact space|compact]] if and only if it is [[closed set|closed]] and bounded.
  1 KB (188 words) - 05:37, 29 December 2008
• Boundary point/Related Articles
  {{r|Closed set}}
  184 bytes (24 words) - 19:07, 30 September 2009
• Cantor set
  ...e middle third of each interval. As a subset of the unit interval it is [[closed set|closed]], [[nowhere dense set|nowhere dense]], [[perfect set|perfect]] and
  2 KB (306 words) - 16:51, 31 January 2011
• Generic point
  ...{''x''} is the whole of ''X'': that is, ''x'' does not lie in any proper [[closed set]] in ''X''. ...y be seen in the [[Zariski topology]] on an algebraic variety, where the [[closed set]]s are the [[zero set]]s of polynomial equations.
  1 KB (240 words) - 20:00, 7 February 2009