Simple space

This article defines a property of topological spaces: a property that can be evaluated to true/false for any topological space|View a complete list of properties of topological spaces

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

Weaker properties

• Space with Abelian fundamental group
• Path-connected space