Space with homology of finite type

From Topospaces
Jump to: navigation, search
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 homology of finite type if all its homology groups are finitely generated. In other words, all its Betti numbers are well-defined and finite.

Relation with other properties

Stronger properties