Definition closed {X:TopologicalSpace} (F:Ensemble (point_set X)) :=
  open (Ensembles.Complement F).

Lemma closed_finite_indexed_union: forall {X:TopologicalSpace} {A:Type} (F:IndexedFamily A (point_set X)), FiniteT A -> (forall a:A, closed (F a)) -> closed (IndexedUnion F).