External characterization of I-favorable spaces

Abstract

We provide both a spectral and an internal characterizations of arbitrary I-favorable spaces with respect to co-zero sets. As a corollary we establish that any product of compact I-favorable spaces with respect to co-zero sets is also I-favorable with respect to co-zero sets. We also prove that every C*-embedded I-favorable with respect to co-zero sets subspace of an extremally disconnected space is extremally disconnected.