Urysohn's Lemma Converse

Lemma
Let $T = \left({X, \vartheta}\right)$ be a topological space.

Let there exist an Urysohn function for any two $A, B \subseteq X$ which are closed sets in $T$ such that $A \cap B = \varnothing$.

Then $T = \left({X, \vartheta}\right)$ is a normal space.

Also see

 * Urysohn's Lemma