Two Applications of Homology Decompositions

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Abstract
We show that a map of rational spaces (see Definition 1) induces a map of homology sections at each stage, and that the k'-invariants are mapped naturally. This is used to characterize rational spaces in which all (matric) Massey products vanish as wedges of rational spheres, and yields the precise Eckmann-Hilton dual of a result of M. Dyer [7]. Berstein's result on co-H spaces [3] is also deduced. These results form a part of the author's doctoral dissertation at Cornell University written under Professor I. Berstein, to whom I express my sincere thanks for his patient help and encouragement. Extensions and counterexamples will appear in a future paper.

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