End Urysohns_Lemma_construction.

(* Specifications: *)
Theorem UrysohnsLemma: forall X:TopologicalSpace, normal_sep X ->
forall F G:Ensemble (point_set X),
closed F -> closed G -> Intersection F G = Empty_set ->
exists f:point_set X -> point_set RTop,
continuous f /\ (forall x:point_set X, 0 <= f x <= 1) /\
(forall x:point_set X, In F x -> f x = 0) /\
(forall x:point_set X, In G x -> f x = 1).