Search results

Jump to navigation Jump to search

Page title matches

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<sub>σ</sub>''' space is similarly a countable [[union]] of [[closed 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]] which is also a G<sub>δ</sub>
    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'''<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
  • 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
  • Norm (mathematics)/Related Articles
    {{r|Closed set}}
    576 bytes (77 words) - 19:04, 11 January 2010
  • Localisation (ring theory)
    ...mplement]] <math>S = R \setminus \mathfrak{p}</math> is a multiplicatively closed set and the localisation of ''R'' at <math>\mathfrak{p}</math> is the localisat
    2 KB (312 words) - 09:18, 21 October 2009
  • Denseness
    ...is, if <math>\scriptstyle \overline{A}=X</math>); equivalently, the only [[closed set]] in ''X'' containing ''A'' is ''X'' itself.
    1 KB (232 words) - 15:27, 6 January 2009
  • Closure (topology)/Related Articles
    {{r|Closed set}}
    288 bytes (41 words) - 15:20, 6 January 2009
  • Continuity
    ...be continuous if for any open set <math>U \in O_Y</math> (respectively, [[closed set|closed subset]] of ''Y'' ) the set <math>f^{-1}(U)=\{ x \in X \mid f(x) \in
    3 KB (614 words) - 14:20, 13 November 2008
  • Totally bounded set/Related Articles
    {{r|Closed set}}
    946 bytes (151 words) - 13:05, 28 December 2008
  • Topological space/Related Articles
    {{r|Closed set}}
    959 bytes (152 words) - 15:06, 28 July 2009
  • Limit point/Related Articles
    {{r|Closed set}}
    518 bytes (68 words) - 18:06, 11 January 2010
  • Topological space
    ...pace|noetherian]]'' if it satisfies the [[descending chain condition]] for closed set: any descending chain of closed subsets <math>Y_0\supseteq Y_1\supseteq\ldo
    15 KB (2,586 words) - 16:07, 4 January 2013
  • Inner product
    ...makes it possible to define the geometric operation of projection onto a [[closed set|closed]] subspace (in the metric topology induced by the inner product), ju
    3 KB (511 words) - 00:25, 20 February 2010
  • Word (language)
    ...n ''their'' definitions, etc. Meaning cannot emerge from definitions in a closed set of words. Without some ‘starter’ words whose meanings do not depend on
    11 KB (1,740 words) - 03:54, 1 November 2011
  • Semantic primes
    ...s, and in fact one cannot define them in simpler words, without creating a closed set of words with a circularity of definitions that ultimately precludes provid ...a circular task, not surprisingly, because the dictionary comprises only a closed set of words, finite in number, that enable descriptions of the meanings of eac
    23 KB (3,578 words) - 14:08, 18 February 2024
  • Space (mathematics)
    ...Borel spaces) are especially useful. Every Borel set (in particular, every closed set and every open set) in a Euclidean space (and more generally, in a complete
    28 KB (4,311 words) - 08:36, 14 October 2010
Retrieved from "https://citizendium.org/wiki/Special:Search"