According to most authors (e.g., Kelley 1955, p. 113; McCarty 1967, p. 144; Willard 1970, p. 92) a regular space is a topological
space in which every neighborhood of a point
contains a closed neighborhood of the same point.

Another equivalent condition is the following: for every closed set and every point there are two disjoint open sets and such that and .

In other sources (e.g., Bourbaki 1989, p. 80; Cullen 1968, p. 113) regularity is defined differently, using separation axioms.