Properties of Hausdorff Space

Theorem

 * Any subspace of a Hausdorff space is Hausdorff.


 * The topological product of two Hausdorff space 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.