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.

Revised on May 15, 2017 12:14:12 by Urs Schreiber (195.37.209.183)