Space with perfect fundamental group

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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: perfect group

This property of topological spaces is defined as the property of the following associated group: first homology group having the following group property: trivial group

Definition

A topological space is said to have perfect fundamental group if it satisfies the following equivalent conditions:

Relation with other properties

Stronger properties