Geodesic
Rosenthal compacta that are premetric of finite degree
Antonio Avilés 1   ; Alejandro Poveda 2   ; Stevo Todorcevic 3
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
Fundamenta Mathematicae, Tome 239 (2017) no. 3, pp. 259-278 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $n=2$.
DOI : 10.4064/fm333-12-2016
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

Antonio Avilés  1   ; Alejandro Poveda  2   ; Stevo Todorcevic  3

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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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

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