End interior_closure.
Arguments interior {X}.
Arguments closure {X}.
Arguments interior_open {X}.
Arguments interior_deflationary {X}.
Arguments interior_fixes_open {X}.
Arguments interior_maximal {X}.
Arguments closure_closed {X}.
Arguments closure_inflationary {X}.
Arguments closure_fixes_closed {X}.
Arguments closure_minimal {X}.
Section interior_closure_relations.
Variable X:TopologicalSpace.

Lemma closure_increasing: forall S T:Ensemble (point_set X),
Included S T -> Included (closure S) (closure T).