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This article defines a homotopy-invariant property of topological spaces, i.e. a property of homotopy classes of topological spaces

View other homotopy-invariant properties of topological spaces OR view all properties of topological spaces


A topological space is termed a homotopy-CW-space if it is homotopy-equivalent to a CW-space, viz a space that can be given the structure of a CW-complex.

Relation with other properties

Stronger properties