Definition object_map := forall gT : finGroupType, {set gT} -> {set gT}.Implicit Types gT hT : finGroupType.(* Group closure. *)
Definition group_valued := forall gT (G : {group gT}), group_set (F G).

(* Specifications: *)
Lemma continuous_is_iso_continuous : continuous -> iso_continuous.
Lemma pcontinuous_is_continuous : pcontinuous -> continuous.
Lemma pcontinuous_is_hereditary : pcontinuous -> hereditary.