Definition:T3 Space/Definition 2

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

$T = \left({S, \tau}\right)$ is $T_3$ iff each open set contains a closed neighborhood around each of its points:


 * $\forall U \in \tau: \forall x \in U: \exists N_x: \complement_S \left({N_x}\right) \in \tau: \exists V \in \tau: x \in V \subseteq N_x \subseteq U$

Also see

 * Equivalence of Definitions of $T_3$ Space