Space with finitely generated homotopy groups

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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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A topological space is said to have finitely generated homotopy groups if each of its homotopy groups is finitely generated (note that for the fundamental group, we require it to be finitely generated as a group; for higher homotopy groups, the finite generation is as an Abelian group).