Parts in $H\sp{\infty }$ with homeomorphic analytic maps

Abstract

Abstract. Hoffman characterized the parts of i/00 as either singleton points or analytic discs. He showed that a part belongs to the latter category if and only if it is hit by the closure of an interpolating sequence and that there are cases where a corresponding analytic map is a homeomorphism and cases where it is not. We show that there is no class, 6, of subsets of the open unit disc such that an analytic map of a part P is a homeomorphism if and only if P is hit by the closure of some set in 6.