\begin{definition}[Definition:Fully Normal Space]
Let $T = \struct {S, \tau}$ be a topological space.
$T$ is '''fully normal''' {{iff}}:
:Every open cover of $S$ has a star refinement
:All points of $T$ are closed.
That is, $T$ is '''fully normal''' {{iff}}:
:$T$ is fully $T_4$
:$T$ is a $T_1$ (Fréchet) space.
{{SeparationAxiomNameVariants||Fully T4|fully $T_4$||fully normal}}
\end{definition}