The Moore space , where is an abelian group and , is a space which has non-trivial (reduced) homology group only in dimension . There is also a cohomology analogue known as a co-Moore space, but this is not defined for all abelian . Spheres are both Moore and co-Moore spaces for .
According to Baues, Moore spaces are -duals to Eilenberg–Mac Lane spaces. This leads to an extensive duality for connected CW complexes.