Urysohn's Lemma Converse

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

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

Then $T = \left({S, \tau}\right)$ is a $T_4$ space.

Also see

 * Urysohn's Lemma