Space with finitely generated homology

Definition
A topological space is said to have finitely generated homology if it has only finitely many nonzero homology groups, and each of them is a finitely generated group. In other words, the Betti numbers are all finite and only finitely many of them are nonzero.

Stronger properties

 * Compact manifold
 * Finite CW-space

Weaker properties

 * Space with homology of finite type
 * Space with finitely generated homology groups