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 $K$ 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 $S_n(I)$ or the Alexandroff $n$-plicate $D_n(2^{\mathbb N})$. This generalizes a result of the third author that corresponds to the case $n=2$.
