1Departamento de Matemáticas Universidad de Murcia 30100 Murcia, Spain 2Departament de Matemàtiques i Informàtica Universitat de Barcelona Gran Via de les Corts Catalanes 585 08007 Barcelona, Spain 3Department of Mathematics University of Toronto M5S 3G3 Toronto, Canada and Institut de Mathématiques de Jussieu CNRS UMR 7586 Case 247 4 Place Jussieu 75252 Paris, France
Fundamenta Mathematicae, Tome 239 (2017) no. 3, pp. 259-278
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 $n=2$.
Keywords:
separable rosenthal compactum continuous n to one preimage metric compactum continuous n to one preimage contains closed subset homeomorphic either n split interval alexandroff n plicate mathbb generalizes result third author corresponds
1
Departamento de Matemáticas Universidad de Murcia 30100 Murcia, Spain
2
Departament de Matemàtiques i Informàtica Universitat de Barcelona Gran Via de les Corts Catalanes 585 08007 Barcelona, Spain
3
Department of Mathematics University of Toronto M5S 3G3 Toronto, Canada and Institut de Mathématiques de Jussieu CNRS UMR 7586 Case 247 4 Place Jussieu 75252 Paris, France
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author = {Antonio Avil\'es and Alejandro Poveda and Stevo Todorcevic},
title = {Rosenthal compacta that are premetric of finite degree},
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Antonio Avilés; Alejandro Poveda; Stevo Todorcevic. Rosenthal compacta that are premetric of finite degree. Fundamenta Mathematicae, Tome 239 (2017) no. 3, pp. 259-278. doi: 10.4064/fm333-12-2016
