\begin{definition}[Definition:Semiregular Space]
Let $T = \struct {S, \tau}$ be a topological space.
$\struct {S, \tau}$ is a '''semiregular space''' {{iff}}:
:$\struct {S, \tau}$ is a Hausdorff ($T_2$) space
:The regular open sets of $T$ form a basis for $T$.
\end{definition}