fact: Record TopologicalSpace : Type := { point_set :> Type; open : Ensemble point_set -> Prop; open_family_union : forall F : Family point_set, (forall S : Ensemble point_set, In F S -> open S) -> open (FamilyUnion F); open_intersection2: forall U V:Ensemble point_set, open U -> open V -> open (Intersection U V); open_full : open Full_set }.
imports: ZornsLemma(FiniteIntersections Powerset_facts)