\begin{definition}[Definition:Regular Space]
Let $T = \struct {S, \tau}$ be a topological space.
$\struct {S, \tau}$ is a '''regular space''' {{iff}}:
:$\struct {S, \tau}$ is a $T_3$ space
:$\struct {S, \tau}$ is a $T_0$ (Kolmogorov) space.
That is:
:$\forall F \subseteq S: \relcomp S F \in \tau, y \in \relcomp S F: \exists U, V \in \tau: F \subseteq U, y \in V: U \cap V = \O$ 
:$\forall x, y \in S$, either:
::$\exists U \in \tau: x \in U, y \notin U$
::$\exists U \in \tau: y \in U, x \notin U$
{{SeparationAxiomNameVariants||T3|$T_3$||regular}}
\end{definition}