Simple space: Difference between revisions
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* It is [[path-connected space|path-connected]] | * It is [[path-connected space|path-connected]] | ||
* The [[fundamental group]] is [[Abelian group|Abelian]] | * The [[fundamental group]] is [[Abelian group|Abelian]] | ||
* The fundamental group acts trivially on all the higher homotopy groups | * The fundamental group [[actions of the fundamental group|acts]] trivially on all the higher homotopy groups | ||
==Relation with other properties== | ==Relation with other properties== | ||
Revision as of 22:54, 21 December 2007
This article defines a homotopy-invariant property of topological spaces, i.e. a property of homotopy classes of topological spaces
View other homotopy-invariant properties of topological spaces OR view all 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
- Aspherical space with Abelian fundamental group