Editing Open set (section)

== Uses ==

Open sets have a fundamental importance in [[topology]]. The concept is required to define and make sense of [[topological space]] and other topological structures that deal with the notions of closeness and convergence for spaces such as [[metric spaces]] and [[uniform spaces]].

Every [[subset]] ''A'' of a topological space ''X'' contains a (possibly empty) open set; the maximum (ordered under inclusion) such open set is called the [[topological interior|interior]] of ''A''. 
It can be constructed by taking the union of all the open sets contained in ''A''.{{sfn|Munkres|2000|pp=95}}

A [[Function (mathematics)|function]] <math>f : X \to Y</math> between two topological spaces <math>X</math> and <math>Y</math> is {{em|[[Continuous function (topology)|continuous]]}} if the [[preimage]] of every open set in <math>Y</math> is open in <math>X.</math>{{sfn|Munkres|2000|pp=102}}
The function <math>f : X \to Y</math> is called {{em|[[Open map|open]]}} if the [[Image (mathematics)|image]] of every open set in <math>X</math> is open in <math>Y.</math>

An open set on the [[real line]] has the characteristic property that it is a countable union of disjoint open intervals.