In algebraic topology, a branch of mathematics, Moore space is the name given to a particular type of topological space that is the homology analogue of the Eilenberg–Maclane spaces of homotopy theory, in the sense that it has only one nonzero homology (rather than homotopy) group.
Given an abelian group G and an integer n ≥ 1, let X be a CW complex such that and for i ≠ n, where
denotes the n-th singular homology group of X and
is the i-th reduced homology group.
It's also sensible to require (as Moore did) that X be simply-connected if n>1.