Section interior_closure_relations.
Definition idempotent {T:Type} (f:T->T) := forall x, f (f x) = f x.
Hint Unfold idempotent : closure.
Variable X:TopologicalSpace.

Lemma closure_intersection: forall S T:Ensemble (point_set X),
Included (closure (Intersection S T))
(Intersection (closure S) (closure T)).