Rosenthal compacta that are premetric of finite degree
Volume 239 / 2017
Fundamenta Mathematicae 239 (2017), 259-278
MSC: 26A21, 54H05, 54D30, 05D10.
DOI: 10.4064/fm333-12-2016
Published online: 5 June 2017
Abstract
We show that if a separable Rosenthal compactum 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 S_n(I) or the Alexandroff n-plicate D_n(2^{\mathbb N}). This generalizes a result of the third author that corresponds to the case n=2.
