End continuous_factorization.
Arguments continuous_factorization {X} {Y}.
Section continuous_surj_factorization.
Variable X Y:TopologicalSpace.
Variable f:point_set X -> point_set Y.
Hypothesis f_cont: continuous f.
Definition continuous_surj_factorization :
point_set X -> point_set (SubspaceTopology (Im Full_set f)).
apply continuous_factorization with f.
intros.
exists x.
constructor.
trivial.
Defined.

Lemma continuous_surj_factorization_is_continuous:
continuous continuous_surj_factorization.