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