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• Open set
  In mathematics, an '''open set''' can be informally described as a [[set]] that does not contain its bound ...e in the ''axiomatic'' way, by enumerating properties of an object called 'open set'. For this approach see [[topological space]].
  1 KB (172 words) - 19:16, 24 March 2008
• Open set/Approval
  12 bytes (1 word) - 09:03, 12 November 2007
• Open set/Definition
  122 bytes (19 words) - 19:12, 30 September 2009
• Open set/Related Articles
  57 bytes (6 words) - 19:17, 24 March 2008

Page text matches

• Open (disambiguation)
  {{rpl|Open set}}
  369 bytes (50 words) - 06:50, 24 September 2013
• Open map/Definition
  ...tion between two topological spaces which sends each open set of one to an open set of the other.
  138 bytes (22 words) - 10:31, 4 September 2009
• Open set
  In mathematics, an '''open set''' can be informally described as a [[set]] that does not contain its bound ...e in the ''axiomatic'' way, by enumerating properties of an object called 'open set'. For this approach see [[topological space]].
  1 KB (172 words) - 19:16, 24 March 2008
• Door space
  ...'''door space''' is 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
• Closed set/Definition
  ...set that contains its [[boundary point|boundary]]; the complement of an [[open set]].
  150 bytes (21 words) - 19:23, 30 September 2009
• Borel set
  ...gebra]] generated by the open sets of a [[topological space]]. Thus, every open set is a Borel set, as are countable unions of open sets (i.e., unions of count
  981 bytes (168 words) - 13:28, 26 July 2008
• Cocountable topology
  ...ology''' is the [[topology]] on a [[set (mathematics)|set]] in which the [[open set]]s are those which have [[countable set|countable]] [[complement (set theor
  1,004 bytes (134 words) - 22:48, 17 February 2009
• Cofinite topology
  ...opology''' is the [[topology]] on a [[set (mathematics)|set]] in the the [[open set]]s are those which have [[finite set|finite]] [[complement (set theory)|com
  1,007 bytes (137 words) - 22:52, 17 February 2009
• Open map
  ...a [[topological space]] which maps every [[open set]] in the domain to an open set in the image.
  1 KB (179 words) - 17:30, 7 February 2009
• Interior (topology)
  ...a subset ''A'' of a [[topological space]] ''X'' is the [[union]] of all [[open set]]s in ''X'' that are [[subset]]s of ''A''. It is usually denoted by <math> * The interior of a open set ''G'' is just ''G'' itself, <math>G = G^{\circ}</math>.
  1 KB (172 words) - 15:44, 7 February 2009
• Compactness axioms
  * '''Compact''' if every cover by [[open set]]s has a finite subcover.
  2 KB (331 words) - 07:47, 30 December 2008
• Compact space/Related Articles
  {{r|Open set}}
  531 bytes (72 words) - 14:37, 31 October 2008
• Closed set
  ...ent (set theory)|complement]] of <math>A</math> in <math>X</math>, is an [[open set]]. The [[empty set]] and the set ''X'' itself are always closed sets. The
  2 KB (338 words) - 15:26, 6 January 2009
• Prime ends
  ...tion is a method to compactify a topological disc (i.e. a simply connected open set in the plane) by adding a circle in an appropriate way. ...with complete proofs. It also introduces a definition which make sense any open set in and dimension.
  1 KB (224 words) - 09:13, 23 January 2009
• Prime ends/Definition
  A method to compactify a topological disc (a simply connected open set in the plane) by adding a circle in an appropriate way.
  162 bytes (26 words) - 14:44, 29 December 2008
• Sober space
  ...is characterised by its [[lattice (order)|lattice]] of [[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
• Closed set/Related Articles
  {{r|Open set}}
  307 bytes (43 words) - 08:34, 2 March 2024
• Separation axioms
  ...s''' describe classes of [[topological space]] according to how well the [[open set]]s of the topology distinguish between distinct points. ...et ''N'' such that ''x'' is in the interior of ''N''; that is, there is an open set ''U'' such that <math>x \in U \subseteq N</math>.
  3 KB (430 words) - 15:28, 6 January 2009
• Boundary point/Related Articles
  {{r|Open set}}
  184 bytes (24 words) - 19:07, 30 September 2009
• G-delta set
  ...ogical space]] which is a [[countability|countable]] [[intersection]] of [[open set]]s. An '''F_σ''' space is similarly a countable [[union]] of [[
  1 KB (223 words) - 13:16, 8 March 2009