Space with abelian fundamental group

Definition
A topological space is said to have Abelian fundamental group if it is path-connected and the fundamental group at any point is Abelian.

Stronger properties

 * Simply connected space
 * Simple space
 * Path-connected topological group

Metaproperties
This corresponds to the algebraic fact that a direct product of Abelian groups is Abelian.

This corresponds to the algebraic fact that a group-theoretic retract of an Abelian group is Abelian.