KC-space: Difference between revisions
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===Stronger properties=== | ===Stronger properties=== | ||
* [[Hausdorff space]]: {{ | * [[Hausdorff space]]: {{proofofstrictimplicationat|[[Hausdorff implies KC]]|[[KC not implies Hausdorff]]}} | ||
===Weaker properties=== | ===Weaker properties=== | ||
* [[US-space]]:{{ | * [[US-space]]:{{proofofstrictimplicationat|[[KC implies US]]|[[US not implies KC]]}} | ||
* [[T1 space]] | * [[T1 space]] | ||
Revision as of 15:20, 21 July 2008
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