Rosenthal compacta that are premetric of finite degree

Abstract

We show that if a separable Rosenthal compactum K is a continuous n-To-one preimage of a metric compactum, but it is not a continuous n-1-To-one preimage, then K contains a closed subset homeomorphic to either the n-split interval Sn(I) or the Alexandroff n-plicate Dn(2N). This generalizes a result of the third author that corresponds to the case n = 2.