CW-space: Difference between revisions
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===Weaker properties=== | ===Weaker properties=== | ||
* [[Normal space]] | * [[Normal space]]: {{proofat|[[CW implies normal]]}} | ||
* [[Hausdorff space]] | * [[Hausdorff space]] | ||
* [[Locally contractible space]] | * [[Locally contractible space]] | ||
* [[Locally path-connected space]] | * [[Locally path-connected space]]: {{proofat|[[CW implies locally path-connected]]}} | ||
* [[Homotopy-CW-space]] | * [[Homotopy-CW-space]] | ||
Revision as of 18:00, 15 December 2007
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
- 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