CW-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

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

• Polyhedron

Weaker properties

• Hereditarily paracompact Hausdorff space
• Paracompact Hausdorff space: For full proof, refer: CW implies paracompact Hausdorff
• Perfectly normal space: For full proof, refer: CW implies perfectly normal
• 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