Aspherical space

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


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Definition

A path-connected space is termed aspherical if it possesses a universal covering space, and if its universal covering space is weakly contractible (equivalently the universal covering space is acyclic; for path-connected simply connected spaces, the two notions are equivalent).