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...ection of commutative rings, the elements of which are 'functions' on each open set of the space.

**In [[mathematical analysis]], a domain is an [[open set]], usually in the [[real number|real]] or [[complex number]]s

...<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:Sug

* A [[basis (topology)|basis]] (or base) for a [[topology]] is a system of [[open set]]s that generate the topology.

...] 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 s

{{r|Open set}}

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 p

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 p

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'' is

...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} </math

In [[complex analysis]], a '''meromorphic function''' on an [[open set|open subset]] ''D'' of the [[complex plane]] is a [[function (mathematics)|

...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: cent

{{r|Open set}}

{{r|Open set}}

...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 metri

...t]] inside the intersection of their domains also agree everywhere in some open set, and

{{r|Open set}}

...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'' &rarr; <math>\m

{{r|Open set}}

...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</