Space with finitely generated homology groups
This article defines a property of topological spaces that depends only on the homology of the topological space, viz it is completely determined by the homology groups. In particular, it is a homotopy-invariant property of topological spaces
View all homology-dependent properties of topological spaces OR view all homotopy-invariant properties of topological spaces OR view all properties of topological spaces
Definition
A topological space is said to have finitely generated homology groups if all its homology groups are finitely generated. Note that the condition of being a space with finitely generated homology is significantly stronger: it requires that there should also be only finitely many nonzero homology groups.