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- ...ection of commutative rings, the elements of which are 'functions' on each open set of the space.162 bytes (25 words) - 19:11, 4 September 2009
- **In [[mathematical analysis]], a domain is an [[open set]], usually in the [[real number|real]] or [[complex number]]s486 bytes (71 words) - 12:37, 31 May 2009
- ...<math>U_y \in O_Y</math> containing the point ''y=f(x)'', there exists an open set <math>U_x \in O_X</math> containing ''x'' such that <math>f(U_x) \subset U_ ...''Y'' ) the set <math>f^{-1}(U)=\{ x \in X \mid f(x) \in U\}</math> is an open set in <math>O_x</math> (respectively, a closed subset of ''X'').[[Category:Sug3 KB (618 words) - 17:00, 1 August 2024
- ...] is short for "Web-based Distributed Authoring and Versioning." It is an open set of extensions to the HTTP protocol that allows remote content editing and s831 bytes (109 words) - 04:14, 14 September 2013
- * A [[basis (topology)|basis]] (or base) for a [[topology]] is a system of [[open set]]s that generate the topology.885 bytes (138 words) - 19:39, 31 January 2009
- {{r|Open set}}308 bytes (40 words) - 17:00, 20 July 2024
- i.e., if it contains an open set that contains the point. ...logical space, a set is a '''neighbourhood''' of a point if it contains an open set that contains the point. <br> (In other words, the open sets containing a p7 KB (1,205 words) - 09:51, 8 September 2013
- i.e., if it contains an open set that contains the point. ...logical space, a set is a '''neighbourhood''' of a point if it contains an open set that contains the point. <br> (In other words, the open sets containing a p7 KB (1,205 words) - 09:52, 8 September 2013
- Let (''X'',''T'') be a topological space with ''T'' the family of [[open set]]s, and let ''A'' be a subset of ''X''. The subspace topology on ''A'' is814 bytes (118 words) - 13:51, 7 February 2009
- {{r|Open set}}946 bytes (151 words) - 13:05, 28 December 2008
- {{r|Open set}}959 bytes (152 words) - 15:06, 28 July 2009
- ...manifold''', is defined as a [[Hausdorff space]] where each point has an [[open set|open]] [[neighborhood (topology)|neighborhood]] which is [[homeomorphism|ho ...tstyle \psi(U_{\alpha} \cap U_{\beta}) \, \in \, \mathbb{R}^n</math> is an open set. The function <math>\psi_{\alpha}: U_{\alpha} \rightarrow V_{\alpha} </math5 KB (809 words) - 12:01, 15 September 2024
- In [[complex analysis]], a '''meromorphic function''' on an [[open set|open subset]] ''D'' of the [[complex plane]] is a [[function (mathematics)|2 KB (233 words) - 07:00, 18 September 2024
- ...structural sheaf <math>O_X=</math> may be constructed as follows. To each open set <math>U</math>, associate the set of functions <div style="text-align: cent3 KB (529 words) - 07:00, 7 July 2024
- ...s use a different definition, in which a neighborhood ''N'' of ''x'' is an open set containing ''x''.</ref> ...''X'' is a collection <math>\mathcal B</math> of open sets such that every open set is a union of elements of <math>\mathcal B</math>. For example, in a metri15 KB (2,586 words) - 16:07, 4 January 2013
- ...t]] inside the intersection of their domains also agree everywhere in some open set, and4 KB (730 words) - 15:17, 8 December 2009
- {{r|Open set}}744 bytes (101 words) - 17:00, 31 August 2024
- ...analysis]]; they are [[function (mathematics)|functions]] defined on an [[open set|open subset]] of the [[complex number|complex number plane]] <math>\mathbb{ If ''U'' is an [[open set|open]] subset of '<math>\mathbb{C}</math> and ''f'' : ''U'' → <math>\m9 KB (1,438 words) - 17:01, 28 August 2024
- ...esidue''' of a function ''f'' [[holomorphic function|holomorphic]] in an open set <math>\Omega</math> with possible exception of a point <math>z_0\in\Omega</1 KB (227 words) - 16:56, 12 November 2008
- ...strongly overlapping. This can be ensured if there is a bounded nonempty open set ''O'' ⊂ ''X'' such that ...e heuristic estimate remains an upper bound if we cannot find a separating open set ''O''.15 KB (2,553 words) - 07:01, 26 August 2024