# Difference between revisions of "Aspherical space"

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==Definition== | ==Definition== | ||

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

## Latest revision as of 19:31, 11 May 2008

This article defines a homotopy-invariant property of topological spaces, i.e. a property of homotopy classes of topological spacesView other homotopy-invariant properties of topological spaces OR view all properties of topological spaces

## 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).