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Convex hyperspaces of probability measures and extensors in the asymptotic category |
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| Authors: | Dušan Repovš Mykhailo Zarichnyi |
| Institution: | a Faculty of Mathematics and Physics, and Faculty of Education, University of Ljubljana, P.O.B. 2964, Ljubljana, 1001, Slovenia b Department of Mechanics and Mathematics, Lviv National University, Universytetska 1, 79000 Lviv, Ukraine c Institute of Mathematics, University of Rzeszów, Rzeszów, Poland |
| Abstract: | The objects of the Dranishnikov asymptotic category are proper metric spaces and the morphisms are asymptotically Lipschitz maps. In this paper we provide an example of an asymptotically zero-dimensional space (in the sense of Gromov) whose space of compact convex subsets of probability measures is not an absolute extensor in the asymptotic category in the sense of Dranishnikov. |
| Keywords: | primary 46E27 46E30 secondary 54C55 54E35 |
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