| Authors: | Avilés, Antonio Poveda, Alejandro Todorčević, Stevo |
Title: | Rosenthal compacta that are premetric of finite degree | Journal: | Fundamenta Mathematicae | Volume: | 239 | Issue: | 3 | First page: | 259 | Last page: | 278 | Issue Date: | 1-Jan-2017 | Rank: | M22 | ISSN: | 0016-2736 | DOI: | 10.4064/fm333-12-2016 | 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 Sn(I) or the Alexandroff n-plicate Dn(2N). This generalizes a result of the third author that corresponds to the case n = 2. |
Keywords: | Alexandroff duplicate | Compact space of the first baire class | Double arrow space | Multidimensional version | Rosenthal compact space | Split interval | Publisher: | Instytut Matematyczny Polskiej Akademii Nauk | Project: | FEDER (No. MTM2014-54182-P) Fundación Séneca - Región de Murcia (No. 19275/PI/14) MECD (Spanish Government) (No. FPU15/00026) Generalitat de Catalunya (No. SGR 437-2014) NSERC (No. 455916) CNRS (No. IMJ-PRG UMR7586) |
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