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- In [[mathematics]], a '''compact space''' is a [[topological space]] for which every covering of that space by a c ==Formal definition of compact space==4 KB (652 words) - 14:44, 30 December 2008
- 32 bytes (3 words) - 14:33, 30 October 2008
- 32 bytes (3 words) - 14:34, 30 October 2008
- 32 bytes (3 words) - 14:35, 30 October 2008
- 413 bytes (51 words) - 14:48, 31 October 2008
- 44 bytes (4 words) - 17:35, 29 December 2008
- 12 bytes (1 word) - 14:37, 31 October 2008
- 120 bytes (17 words) - 14:37, 31 October 2008
- {{r|Sequentially compact space}}531 bytes (72 words) - 14:37, 31 October 2008
- 109 bytes (14 words) - 16:58, 30 October 2008
Page text matches
- * An indiscrete space is [[compact space|compact]].766 bytes (106 words) - 16:04, 4 January 2013
- In [[mathematics]], the '''Heine-Borel theorem''' characterises the [[compact space|compact]] [[subset]]s of the [[real number]]s. ...We may reduce to the case of a closed interval, since a closed subset of a compact space is compact.2 KB (381 words) - 08:54, 29 December 2008
- * A discrete space is [[compact space|compact]] if and only if it is [[finite set|finite]].872 bytes (125 words) - 15:57, 4 January 2013
- 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
- #REDIRECT [[Compact space]]27 bytes (3 words) - 10:56, 25 May 2010
- #REDIRECT [[Compact space]]27 bytes (3 words) - 10:57, 25 May 2010
- #REDIRECT [[Compact space]]27 bytes (3 words) - 13:14, 25 May 2010
- #REDIRECT [[Compact space]]27 bytes (3 words) - 14:37, 31 October 2008
- #REDIRECT [[Compact space/Definition]]38 bytes (4 words) - 14:37, 31 October 2008
- #REDIRECT [[Compact space/Related Articles]]44 bytes (5 words) - 14:37, 31 October 2008
- #REDIRECT [[Compact space#Finite intersection property]]56 bytes (6 words) - 14:25, 30 December 2008
- In [[mathematics]], a '''compact space''' is a [[topological space]] for which every covering of that space by a c ==Formal definition of compact space==4 KB (652 words) - 14:44, 30 December 2008
- An [[infinite set|infinite]] [[Cartesian product]] of non-empty non-[[compact space]]s has the property that every compact subset is nowhere dense.850 bytes (118 words) - 22:30, 20 February 2010
- * [[Compact space|compact]];1,007 bytes (137 words) - 22:52, 17 February 2009
- * Any [[compact space|compact]] metric space is [[sequentially compact space|sequentially compact]] and hence complete. The converse does not hold: for3 KB (441 words) - 12:23, 4 January 2009
- ...d of a topological space ''X'' is a function ''e'' which assigns to each [[compact space|compact]] set ''K'' in ''X'' some [[connected component]] with non-compact1 KB (250 words) - 01:07, 19 February 2009
- {{r|Sequentially compact space}}531 bytes (72 words) - 14:37, 31 October 2008
- {{r|Compact space}}565 bytes (76 words) - 19:05, 11 January 2010
- ...is totally bounded if and only if its [[closure (topology)|closure]] is [[compact space|compact]].975 bytes (166 words) - 15:27, 6 January 2009
- {{r|Compact space}}942 bytes (125 words) - 18:29, 11 January 2010
- ...copies of a two-point space with the [[discrete topology]]. It is thus [[compact space|compact]]. It may be realised as the space of binary sequences As a topological space, the Cantor set is [[uncountable set|uncountable]], [[compact space|compact]], [[second countable space|second countable]] and [[totally discon2 KB (306 words) - 16:51, 31 January 2011
- ...ral topology]], a '''compactification''' of a [[topological space]] is a [[compact space]] in which the original space can be embedded, allowing the space to be stu ...if ''X'' is a [[Tychonoff space]] then any continuous map from ''X'' to a compact space can be extended to a map from β(''X'') compatible with ''e''. This extens2 KB (350 words) - 00:48, 18 February 2009
- ...ates that a subset of the [[Euclidean space]] '''R'''<sup>''n''</sup> is [[compact space|compact]] if and only if it is [[closed set|closed]] and bounded.1 KB (188 words) - 05:37, 29 December 2008
- {{r|Compact space}}689 bytes (88 words) - 17:15, 11 January 2010
- {{r|Compact space}}478 bytes (62 words) - 11:58, 11 January 2010
- {{r|Compact space}}482 bytes (62 words) - 20:41, 11 January 2010
- {{r|Compact space}}497 bytes (64 words) - 19:44, 11 January 2010
- {{r|Compact space}}492 bytes (62 words) - 19:52, 11 January 2010
- * [[Tychonov's Theorem]]: The product of a family of non-empty [[compact space|compact topological space]]s is compact in the [[product topology]].2 KB (266 words) - 13:28, 5 January 2013
- The product of two (and hence finitely many) [[compact space]]s is compact.2 KB (345 words) - 16:47, 6 February 2010
- * [[Compact space|Compactness]];2 KB (265 words) - 07:44, 4 January 2009
- {{r|Compact space}}923 bytes (145 words) - 10:03, 29 December 2008
- {{r|Compact space}}455 bytes (57 words) - 15:35, 11 January 2010
- {{r|Compact space}}946 bytes (151 words) - 13:05, 28 December 2008
- ...'''<sup>d</sup>. He showed that such a system of functions has a unique [[Compact space|compact]] (closed and bounded) fixed set ''S''.2 KB (327 words) - 15:52, 27 October 2008
- {{r|Compact space}}870 bytes (139 words) - 17:44, 29 December 2008
- ; Compactness: {{Main|Compactness axioms}}<math>X</math> is said to be ''[[Compact space|compact]]'' if any open cover of <math>X</math> has a ''finite sub-cover''.15 KB (2,586 words) - 16:07, 4 January 2013
- ...infin; are added to the reals to form the [[extended real number line]], a compact space which is not a field but retains many of the properties of the real numbers19 KB (2,948 words) - 10:07, 28 February 2024
- * [[compact space]]s (and compact Hausdorff spaces, i.e. compact <math>\ T_2</math>-spaces);45 KB (7,747 words) - 06:00, 17 October 2013
- During this period, a method of manufacturing many transistors in a compact space gained popularity. The [[integrated circuit]] ('''IC''') allowed a large n17 KB (2,465 words) - 20:44, 28 July 2010