Simple space

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

Stronger properties

 * Simply connected space
 * Aspherical space with Abelian fundamental group

Weaker properties

 * Space with Abelian fundamental group
 * Path-connected space

Textbook references

 * , Page 140 (formal definition)
 * , Page 342 (definition in paragraph): Hatcher uses the term Abelian space locally in the book
 * , Page 384 (definition in paragraph)