Definition:T3 Space/Definition 3

Definition
Let $T = \left({S, \tau}\right)$ be a topological space.

$T = \left({S, \tau}\right)$ is $T_3$ iff each of its closed sets is the intersection of its closed neighborhoods.
 * $\forall H \subseteq S: \complement_S \left({H}\right) \in \tau: H = \bigcap \left\{{N_H: \complement_S \left({N_H}\right) \in \tau, \exists V \in \tau: H \subseteq V \subseteq N_H}\right\}$

Also see

 * Equivalence of Definitions of $T_3$ Space