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Rosenthal compacta that are premetric of finite degree

Volume 239 / 2017

Antonio Avilés, Alejandro Poveda, Stevo Todorcevic Fundamenta Mathematicae 239 (2017), 259-278 MSC: 26A21, 54H05, 54D30, 05D10. DOI: 10.4064/fm333-12-2016 Published online: 5 June 2017


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 $n=2$.


  • Antonio AvilésDepartamento de Matemáticas
    Universidad de Murcia
    30100 Murcia, Spain
  • Alejandro PovedaDepartament de Matemàtiques i Informàtica
    Universitat de Barcelona
    Gran Via de les Corts Catalanes 585
    08007 Barcelona, Spain
  • Stevo TodorcevicDepartment of Mathematics
    University of Toronto
    M5S 3G3 Toronto, Canada
    Institut de Mathématiques de Jussieu
    CNRS UMR 7586 Case 247
    4 Place Jussieu
    75252 Paris, France

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