# Condition for Open Extension Space to be T5 Space

## Theorem

Let $T = \struct {S, \tau}$ be a topological space.

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

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