T4 Property is not Hereditary

Theorem
Let $T = \left({S, \tau}\right)$ be a topological space which is a $T_4$ space.

Let $T_H = \left({H, \tau_H}\right)$, where $\varnothing \subset H \subseteq S$, be a subspace of $T$.

Then it does not necessarily follow that $T_H$ is a $T_4$ space.