Definition open_map {X Y:TopologicalSpace}
  (f:point_set X -> point_set Y) : Prop :=
forall U:Ensemble (point_set X), open U -> open (Im U f).

(* Specifications: *)
Lemma homeomorphism_is_open_map: forall {X Y:TopologicalSpace} (f:point_set X -> point_set Y), homeomorphism f -> open_map f.
Lemma invertible_open_map_is_homeomorphism: forall {X Y:TopologicalSpace} (f:point_set X -> point_set Y), invertible f -> continuous f -> open_map f -> homeomorphism f.