KC-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

This is a variation of Hausdorffness. View other variations of Hausdorffness

Definition

Symbol-free definition

A topological space is termed a KC-space if every compact subset of it is closed (here, by compact subset, we mean a subset which is a compact space under the subspace topology).

Relation with other properties

Stronger properties

• Hausdorff space: For proof of the implication, refer Hausdorff implies KC and for proof of its strictness (i.e. the reverse implication being false) refer KC not implies Hausdorff

Weaker properties

• US-space:For proof of the implication, refer KC implies US and for proof of its strictness (i.e. the reverse implication being false) refer US not implies KC
• T1 space