Contents

Statement

Proposition

Let $(X,\tau)$ be a compact Hausdorff topological space and let $Y \subset X$ be a topological subspace. Then the following are equivalent:

1. $Y \subset X$ is a closed subspace;

2. $Y$ is a compact topological space.

Proof

The two directions to be proven are

See the proofs there.

Revision on April 13, 2017 at 16:32:47 by Urs Schreiber See the history of this page for a list of all contributions to it.