\begin{definition}[Definition:Perfectly T4 Space]
Let $T = \struct {S, \tau}$ be a topological space.
$T$ is a '''perfectly $T_4$ space''' {{iff}}:
:$(1): \quad T$ is a $T_4$ space
:$(2): \quad$ 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 $T$.
\end{definition}