 In fact, given a set "X" and a collection F of subsets of "X" that has these properties, then F will be the collection of closed sets for a unique topology on "X".The intersection property also allows one to define the closure of a set "A" in a space "X", which is defined as the smallest closed subset of "X" that is a superset of "A".Specifically, the closure of "A" can be constructed as the intersection of all of these closed supersets.