# Space with homology of finite type

From Topospaces

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 spacesView 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 **homology of finite type** if all its homology groups are finitely generated. In other words, all its Betti numbers are well-defined and finite.