Condition for Open Extension Space to be T5 Space

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

Let $T^*_{\bar p} = \left({S^*_p, \tau^*_{\bar p}}\right)$ be the open extension space of $T$.

Then $T^*_{\bar p}$ is a $T_5$ space $T$ is a $T_5$ space.