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 complement_inclusion: forall {Y:Type} (S T:Ensemble Y),
Included S T -> Included (Complement T) (Complement S).