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.
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