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- In [[mathematics]], a '''topological space''' is an [[ordered pair]] <math>(X,\mathcal T)</math> where <math>X</math> A topological space is an ordered pair <math>(X,\mathcal T)</math> where <math>X</math> is a se15 KB (2,586 words) - 16:07, 4 January 2013
- #REDIRECT [[Topological space]]31 bytes (3 words) - 09:46, 5 December 2007
- 141 bytes (19 words) - 17:39, 17 June 2009
- 12 bytes (1 word) - 02:14, 14 October 2007
- 804 bytes (100 words) - 02:27, 1 November 2008
- 959 bytes (152 words) - 15:06, 28 July 2009
Page text matches
- #REDIRECT [[Topological space#Some topological notions]]56 bytes (6 words) - 07:03, 29 December 2008
- In [[topology]], an '''indiscrete space''' is a [[topological space]] with the '''indiscrete topology''', in which the only open [[subset]]s ar * Every map from a topological space to an indiscrete space is [[continuous map|continuous]].766 bytes (106 words) - 16:04, 4 January 2013
- {{r|Topological space}}359 bytes (48 words) - 15:04, 28 July 2009
- Properties that a topological space may satisfy which refer to the countability of certain structures within th155 bytes (21 words) - 01:18, 18 February 2009
- In a [[topological space]], a subset whose [[closure]] (i.e., all boundary points added) is the whol145 bytes (21 words) - 17:34, 24 August 2009
- In [[topology]], a '''discrete space''' is a [[topological space]] with the '''discrete topology''', in which every [[subset]] is open. * Every map from a discrete space to a topological space is [[continuous map|continuous]].872 bytes (125 words) - 15:57, 4 January 2013
- #REDIRECT [[Topological space]]31 bytes (3 words) - 09:46, 5 December 2007
- A compact space in which a given topological space can be embedded as a dense subset.121 bytes (19 words) - 17:30, 5 January 2009
- <noinclude>{{Subpages}}</noinclude>A topological space in which the only open subsets are the empty set and the space itself124 bytes (20 words) - 15:59, 4 January 2013
- A topological space which is a countable union of nowhere dense subsets; a meagre space.124 bytes (18 words) - 16:22, 3 January 2009
- A '''ringed space''' is a topological space <math>X</math> together with a sheaf of rings <math>F</math>.118 bytes (20 words) - 21:49, 22 January 2008
- ...hich are also "distant". In [[differential geometry]], this means that one topological space can be deformed into the other by "bending" and "stretching".2 KB (265 words) - 07:44, 4 January 2009
- Two continuous deformed functions from one topological space into another.111 bytes (13 words) - 08:48, 4 September 2009
- A topological space in which each subset is open or closed.95 bytes (14 words) - 07:57, 28 December 2008
- Any topological space which has a metric defined on it.92 bytes (13 words) - 09:56, 4 September 2009
- A topological space that is T4 but not countably paracompact.97 bytes (13 words) - 14:53, 29 October 2008
- In [[general topology]], a '''nowhere dense set''' in a topological space is a set whose [[closure (topology)|closure]] has empty [[interior (topolog ...is a [[countability|countable]] [[union]] of nowhere dense sets: any other topological space is of '''second category'''. The ''[[Baire category theorem]]'' states tha850 bytes (118 words) - 22:30, 20 February 2010
- A topological space in which closed subsets satisfy the descending chain condition.120 bytes (15 words) - 10:15, 4 September 2009
- A topological space with the discrete topology, in which every subset is open (and also closed)132 bytes (19 words) - 07:58, 28 December 2008
- A topological space which is not the countable union of nowhere dense subsets; a space which is154 bytes (24 words) - 16:23, 3 January 2009
- A topological space with a countable dense subset.86 bytes (11 words) - 17:52, 1 December 2008
- A topological space in which every sequence has a convergent subsequence.109 bytes (14 words) - 16:58, 30 October 2008
- A set in a topological space whose closure has empty interior.98 bytes (14 words) - 02:35, 29 December 2008
- #REDIRECT [[Topological space#Bases and sub-bases]]51 bytes (6 words) - 02:31, 27 November 2008
- #REDIRECT [[Topological space#Bases and sub-bases]]51 bytes (6 words) - 02:30, 27 November 2008
- A topological space in which every irreducible closed set has a unique generic point.121 bytes (17 words) - 12:25, 31 December 2008
- A property that describes how good points in a topological space can be distinguished.122 bytes (17 words) - 17:30, 17 June 2009
- A topological space in which there is no non-trivial subset which is both open and closed.126 bytes (19 words) - 17:26, 8 December 2008
- Function on a directed set into a topological space which generalises the notion of sequence.130 bytes (18 words) - 10:10, 4 September 2009
- In [[general topology]], a '''G<sub>δ</sub> set''' is a [[subset]] of a [[topological space]] which is a [[countability|countable]] [[intersection]] of [[open set]]s. A '''G<sub>δ</sub> space''' is a topological space in which every closed set is a G<sub>δ</sub> set. A [[normal space]] whic1 KB (223 words) - 13:16, 8 March 2009
- Axioms for a topological space which specify how well separated points and closed sets are by open sets.140 bytes (21 words) - 07:15, 2 November 2008
- Topological space with additional structure which is used to define uniform properties such a189 bytes (23 words) - 20:36, 4 September 2009
- An assignment of open sets to a subset of a topological space.99 bytes (15 words) - 19:58, 4 September 2009
- The union of all open sets contained within a given subset of a topological space.118 bytes (18 words) - 16:26, 27 December 2008
- The finest topology on the image set that makes a surjective map from a topological space continuous.137 bytes (20 words) - 11:53, 31 December 2008
- A set that belongs to the σ-algebra generated by the open sets of a topological space.123 bytes (19 words) - 18:52, 24 June 2008
- {{r|Topological space}}531 bytes (72 words) - 14:37, 31 October 2008
- The Cantor set may be considered a [[topological space]], [[homeomorphism|homeomorphic]] to a product of [[countable set|countably As a topological space, the Cantor set is [[uncountable set|uncountable]], [[compact space|compact2 KB (306 words) - 16:51, 31 January 2011
- For a topological space this generalises the notion of "point at infinity" of the real line or plan137 bytes (21 words) - 01:09, 19 February 2009
- ...to the [[sigma algebra|σ-algebra]] generated by the open sets of a [[topological space]]. Thus, every open set is a Borel set, as are countable unions of open set ...math>O</math> are the open sets of <math>X</math> (or, equivalently, the [[topological space|topology]] of <math>X</math>). Then <math>A \subset X </math> is a Borel se981 bytes (168 words) - 13:28, 26 July 2008
- ...bsolute G<sub>δ</sub>'', that is, a [[G-delta set|G<sub>δ</sub>]] in every topological space in which it can be embedded.3 KB (441 words) - 12:23, 4 January 2009
- A subset of a topological space that is a countable intersection of open sets.115 bytes (17 words) - 08:07, 4 September 2009
- A set in a topological space with no isolated points, so that all its points are limit points of itself.140 bytes (23 words) - 02:34, 29 December 2008
- A point of a topological space which is not contained in any proper closed subset; a point satisfying no s160 bytes (24 words) - 20:02, 7 February 2009
- '''Countability axioms in topology''' are properties that a [[topological space]] may satisfy which refer to the [[countable set|countability]] of certain677 bytes (96 words) - 01:19, 18 February 2009
- Topological space together with commutative rings for all its open sets, which arises from 'g201 bytes (27 words) - 19:14, 4 September 2009
- ...a [[topological space]] ''X'' is the set union of ''A'' and ''all'' its [[topological space#Some topological notions|limit points]] in ''X''. It is usually denoted by1 KB (184 words) - 15:20, 6 January 2009
- A point which cannot be separated from a given subset of a topological space; all neighbourhoods of the points intersect the set.165 bytes (25 words) - 02:16, 6 December 2008
- In a topological space, a set containing a given point in its interior, expressing the idea of poi156 bytes (24 words) - 18:54, 28 May 2009
- {{r|Topological space}}942 bytes (125 words) - 18:29, 11 January 2010