# Simple space

From Topospaces

This article defines a homotopy-invariant property of topological spaces, i.e. a property of homotopy classes of topological spacesView other homotopy-invariant properties of topological spaces OR view all properties of topological spaces

## Contents

## Definition

A topological space is termed **simple** if it satisfies the following three conditions:

- It is path-connected
- The fundamental group is Abelian
- The fundamental group acts trivially on all the higher homotopy groups

## Relation with other properties

### Stronger properties

- Simply connected space
- Aspherical space with Abelian fundamental group