Definition:T3 Space/Definition 2

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

$T = \struct {S, \tau}$ is $T_3$ each open set contains a closed neighborhood around each of its points:


 * $\forall U \in \tau: \forall x \in U: \exists N_x: \relcomp S {N_x} \in \tau: \exists V \in \tau: x \in V \subseteq N_x \subseteq U$

where $N_x$ denotes a neighborhood of $x$.

Also see

 * Equivalence of Definitions of $T_3$ Space