proposition: Lemma continuous_surj_factorization_is_surjective: surjective continuous_surj_factorization.
proof: Proof. intro. destruct y. destruct i. exists x. unfold continuous_surj_factorization, continuous_factorization. subst. f_equal. f_equal. apply proof_irrelevance. Qed.
imports: ZornsLemma(EnsemblesTactics) TopologicalSpaces Continuity SubspaceTopology