Regular space

Regular space: A topological space is termed regular if all points are closed sets (the $T_{1}$ assumption), and, given a point and a closed set not containing it, there are disjoint open sets containing the point and closed set respectively.

In some definitions, the $T_{1}$ assumption is skipped.

Related terms: regularity (the property of a topological space being regular)

Primary subject wiki entry: Topospaces:Regular space

Also located at: Wikipedia:Regular space, Planetmath:RegularSpace, Mathworld:RegularSpace