Inductive homeomorphic (X Y:TopologicalSpace) : Prop :=
| intro_homeomorphic: forall f:point_set X -> point_set Y,
    homeomorphism f -> homeomorphic X Y.Inductive homeomorphic (X Y:TopologicalSpace) : Prop :=
| intro_homeomorphic: forall f:point_set X -> point_set Y,
    homeomorphism f -> homeomorphic X Y.

(* Specifications: *)
Lemma homeomorphic_equiv: equivalence homeomorphic.