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 interior_intersection: forall S T:Ensemble (point_set X),
interior (Intersection S T) =
Intersection (interior S) (interior T).