Definition:Hausdorff Space

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

Also known as
This condition is known as the Hausdorff condition.

For short, $T$ is Hausdorff is used to mean $T$ is a Hausdorff space.

Conveniently, a topological space is Hausdorff if any two distinct points can be housed off from one another in separate disjoint open sets.

Equivalence of Definitions
See Equivalence of Definitions of $T_2$ Space for a proof that the two definitions are equivalent.

Also see

 * Basic Properties of Hausdorff Space