G_δ space

In mathematics, particularly topology, a G_δ space is a topological space in which closed sets are in a way ‘separated’ from their complements using only countably many open sets. A G_δ space may thus be regarded as a space satisfying a different kind of separation axiom. In fact normal G_δ spaces are referred to as perfectly normal spaces, and satisfy the strongest of separation axioms.

G_δ spaces are also called perfect spaces. The term perfect is also used, incompatibly, to refer to a space with no isolated points; see Perfect set.