proposition: Lemma strong_topology_continuous_char (Z : TopologicalSpace) (g : point_set StrongTopology -> point_set Z) : continuous g <-> forall a, continuous (compose g (f a)).
proof: Proof. split. - intros. unfold compose. apply continuous_composition; auto. apply strong_topology_makes_continuous_funcs. - intros. red; intros. simpl. red. intros. rewrite <- inverse_image_composition. apply H. assumption. Qed.
imports: TopologicalSpaces Continuity