CW-space: Difference between revisions
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===Weaker properties=== | ===Weaker properties=== | ||
* [[Hereditarily paracompact Hausdorff space]] | |||
* [[Paracompact Hausdorff space]]: {{proofat|[[CW implies paracompact Hausdorff]]}} | * [[Paracompact Hausdorff space]]: {{proofat|[[CW implies paracompact Hausdorff]]}} | ||
* [[Normal space]]: {{proofat|[[CW implies normal]]}} | * [[Normal space]]: {{proofat|[[CW implies normal]]}} | ||
Revision as of 20:15, 16 January 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
Definition
A topological space is said to be a CW-space if it possesses a CW-decomposition, or in other words, if it can be viewed as the underlying topological space of a CW-complex.
Relation with other properties
Stronger properties
Weaker properties
- Hereditarily paracompact Hausdorff space
- Paracompact Hausdorff space: For full proof, refer: CW implies paracompact Hausdorff
- Normal space: For full proof, refer: CW implies normal
- Hausdorff space
- Locally contractible space
- Locally path-connected space: For full proof, refer: CW implies locally path-connected
- Homotopy-CW-space