On the dimension of almost -dimensional spaces

Oversteegen and Tymchatyn proved that homeomorphism groups of positive dimensional Menger compacta are -dimensional by proving that almost -dimensional spaces are at most -dimensional. These homeomorphism groups are almost -dimensional and at least -dimensional by classical results of Brechner and Bestvina. In this note we prove that almost -dimensional spaces for are -dimensional. As a corollary we answer in the affirmative an old question of R. Duda by proving that every hereditarily locally connected, non-degenerate, separable, metric space is -dimensional.