Acyclic space

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.

Metaproperties
A product of acyclic spaces is acyclic. The proof of this relies on the Kunneth formula.