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- 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
- 12 bytes (1 word) - 09:03, 12 November 2007
- 122 bytes (19 words) - 19:12, 30 September 2009
- 57 bytes (6 words) - 19:17, 24 March 2008
Page text matches
- {{rpl|Open set}}369 bytes (50 words) - 06:50, 24 September 2013
- ...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
- 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''' is a [[topological space]] in which each [[subset]] is [[open set|open]] or [[closed set|closed]] or both.654 bytes (99 words) - 12:01, 8 August 2024
- ...set that contains its [[boundary point|boundary]]; the complement of an [[open set]].150 bytes (21 words) - 19:23, 30 September 2009
- ...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 count1,012 bytes (172 words) - 12:01, 20 July 2024
- ...ology''' is the [[topology]] on a [[set (mathematics)|set]] in which the [[open set]]s are those which have [[countable set|countable]] [[complement (set theor1 KB (138 words) - 07:01, 30 July 2024
- ...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)|com1 KB (141 words) - 12:00, 30 July 2024
- ...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
- ...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 (176 words) - 17:01, 1 September 2024
- * '''Compact''' if every cover by [[open set]]s has a finite subcover.2 KB (335 words) - 12:00, 31 July 2024
- ...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. The2 KB (342 words) - 17:01, 29 July 2024
- {{r|Open set}}627 bytes (85 words) - 12:00, 31 July 2024
- {{r|Open set}}508 bytes (71 words) - 17:01, 29 July 2024
- ...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
- 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
- ...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
- ...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
- ...ogical space]] for which every covering of that space by a collection of [[open set]]s has a finite subcovering. If the space is a [[metric space]] then compac ...cal space may be defined in terms of the [[closed set]]s rather than the [[open set]]s, so we may transpose the definition of compactness in terms of open sets4 KB (656 words) - 12:00, 31 July 2024
- ...ogical space]] which is a [[countability|countable]] [[intersection]] of [[open set]]s. An '''F<sub>σ</sub>''' space is similarly a countable [[union]] of [[1 KB (227 words) - 17:00, 19 August 2024