Definition:Regular Space

Definition
Let $T = \struct {S, \tau}$ be a topological space.

$\struct {S, \tau}$ is a regular space :
 * $\struct {S, \tau}$ 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:
 * $\exists U \in \tau: x \in U, y \notin U$
 * $\exists U \in \tau: y \in U, x \notin U$

Also see

 * Definition:Separation Axioms