Definition:T3 Space/Definition 3

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

$T = \struct {S, \tau}$ is $T_3$ each of its closed sets is the intersection of its closed neighborhoods:
 * $\forall H \subseteq S: \relcomp S H \in \tau: H = \bigcap \set {N_H: \relcomp S H \in \tau, \exists V \in \tau: H \subseteq V \subseteq N_H}$

Also see

 * Equivalence of Definitions of $T_3$ Space