Compact Hausdorff space

This article defines a property of topological spaces: a property that can be evaluated to true/false for any topological space|View a complete list of properties of topological spaces

Definition

A topological space is termed compact Hausdorff if it satisfies the following equivalent conditions:

• It is compact and Hausdorff
• A subset is closed iff it is compact in the subspace topology

Relation with other properties

Stronger properties

• Compact metrizable space

Weaker properties

• Baire space
• Locally compact Hausdorff space
• Paracompact Hausdorff space
• Normal space