Definition Urysohns_Lemma_function : point_set X -> point_set RTop.

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).