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_union: forall S T:Ensemble (point_set X),
Included (Union (interior S) (interior T))
(interior (Union S T)).