A Remark on the Genus of the Infinite Quaternionic Projective Space

It is shown that only countably many spaces in the genus of , the infinite quaternionic projective space, can admit essential maps from , the infinite complex projective space. Examples of countably many homotopically distinct spaces in the genus of which admit essential maps from are constructed. These results strengthen a theorem of McGibbon and Rector which states that among the uncountably many homotopy types in its genus, is the only one which admits a maximal torus