Acyclic space
This article defines a homotopy-invariant property of topological spaces, i.e. a property of homotopy classes of topological spaces
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This is a variation of contractibility. View other variations of contractibility
Definition
A topological space is said to be acyclic if the homology groups in all dimensions are the same as those of a point, for any homology theory. Equivalently, it suffices to say that the singular homology groups are the same as those for a point.