Locally compact Hausdorff space: Difference between revisions
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{{topospace property}} | {{topospace property conjunction|locally compact space|Hausdorff space}} | ||
==Definition== | ==Definition== | ||
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===Weaker properties=== | ===Weaker properties=== | ||
* [[Completely regular space]] | * [[Completely regular space]]: {{proofat|[[locally compact Hausdorff implies completely regular]]}} | ||
* [[Locally normal space]] | * [[Locally normal space]] | ||
* [[Baire space]] | * [[Baire space]]: {{proofat|[[Locally compact Hausdorff implies Baire]]}} | ||
* [[Locally compact space]] | * [[Locally compact space]] | ||
* [[Strongly locally compact space]] | * [[Strongly locally compact space]] | ||
Latest revision as of 19:48, 11 May 2008
This article describes a property of topological spaces obtained as a conjunction of the following two properties: locally compact space and Hausdorff space
Definition
A topological space is termed locally compact Hausdorff if it satisfies the following equivalent conditions:
- It is locally compact and Hausdorff
- It is strongly locally compact and Hausdorff
- It has a one-point compactification
Relation with other properties
Stronger properties
Weaker properties
- Completely regular space: For full proof, refer: locally compact Hausdorff implies completely regular
- Locally normal space
- Baire space: For full proof, refer: Locally compact Hausdorff implies Baire
- Locally compact space
- Strongly locally compact space