View source for T2 (Hausdorff)



Every [[compact]] subspace of a Hausdorff space is closed. That is, if <math>Y</math> is a compact subspace of a <math>T_2</math> space <math>X</math>, then <math>Y</math> is a closed subset of <math>X</math>.

(VUT) A continuous bijection from a compact space to a Hausdorff space is a homeomorphism.

Compact Hausdorff spaces are <math>T_4</math>.

<math>T_2</math> is not preserved by quotients, continuous images, or continuous preimages.


Let <math>X</math> be a <math>T_2</math> topological space and let <math>p \in X</math>. Then <math>\{p\}</math> is closed in <math>X</math>.