Space with homology of finite type
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
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A topological space is said to have homology of finite type if all its homology groups are finitely generated. In other words, all its Betti numbers are well-defined and finite.