Kfagerstrom: Created page with " Every compact subspace of a Hausdorff space is closed. That is, if $Y$ is a compact subspace of a $T_2$ space $X$ , then $Y$ i..."

2022-12-07T19:04:25Z

Created page with " 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> i..."

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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>.

T2 (Hausdorff) - Revision history

Kfagerstrom: Created page with " Every compact subspace of a Hausdorff space is closed. That is, if Y is a compact subspace of a T_2 space X, then Y i..."

Kfagerstrom: Created page with " Every compact subspace of a Hausdorff space is closed. That is, if $Y$ is a compact subspace of a $T_2$ space $X$ , then $Y$ i..."