Definition:Completely Hausdorff Space/Definition 1

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

$\struct {S, \tau}$ is a completely Hausdorff space or $T_{2 \frac 1 2}$ space :
 * $\forall x, y \in S, x \ne y: \exists U, V \in \tau: x \in U, y \in V: U^- \cap V^- = \O$

That is, for any two distinct elements $x, y \in S$ there exist open sets $U, V \in \tau$ containing $x$ and $y$ respectively whose closures are disjoint.

Also see

 * Leigh.Samphier/Sandbox/Equivalence of Definitions of Completely Hausdorff Space