fact: Definition compact (X:TopologicalSpace) := forall C:Family X, (forall U:Ensemble X, In C U -> open U) -> FamilyUnion C = Full_set -> exists C':Family X, Finite C' /\ Included C' C /\ FamilyUnion C' = Full_set.
imports: Coq(ClassicalChoice Program.Subset) ZornsLemma(Finite_sets Powerset_facts) Topology(FiltersAndNets)