# Space with torsion-free homology

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 **torsion-free homology** if all its homology groups are torsion-free Abelian groups.

## Relation with other properties

### Stronger properties

- Space with free homology: Note that the two properties are equivalent for a space with homology of finite type