Properties of Hausdorff Space

Theorem

 * Any subspace of a Hausdorff space is Hausdorff.


 * The topological product of two Hausdorff spaces is Hausdorff.


 * If $f: T_1 \to T_2$ is injective and continuous, and $T_2$ is Hausdorff, then so is $T_1$.


 * The Hausdorff condition is a topological property.