Definition:Perfectly T4 Space

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

$\left({X, \vartheta}\right)$ is a perfectly $T_4$ space iff:
 * Every closed set in $T$ is a $G_\delta$ set.

That is:
 * Every closed set in $T$ can be written as a countable intersection of open sets of $T$.