# Aspherical space

From Topospaces

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).