Space with abelian fundamental group

This article defines a homotopy-invariant property of topological spaces, i.e. a property of homotopy classes of topological spaces

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This property of topological spaces is defined as the property of the following associated group: fundamental group having the following group property: Abelian 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.

Relation with other properties

Stronger properties

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

Metaproperties

Products

This property of topological spaces is closed under taking arbitrary products
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This corresponds to the algebraic fact that a direct product of Abelian groups is Abelian.

Retract-hereditariness

This property of topological spaces is hereditary on retracts, viz if a space has the property, so does any retract of it
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This corresponds to the algebraic fact that a group-theoretic retract of an Abelian group is Abelian.