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Hyperspace of convex compacta of nonmetrizable compact convex subspaces of locally convex spaces |
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| Authors: | Lidia Bazylevych Michael Zarichnyi |
| Institution: | a National University “Lviv Polytechnica”, 12 Bandery Str., 79013 Lviv, Ukraine b Institute of Mathematics, Physics and Mechanics, and Faculty of Education, University of Ljubljana, P.O. Box 2964, Ljubljana, Slovenia 1001 c Department of Mechanics and Mathematics, Lviv National University, Universytetska Str. 1, 79000 Lviv, Ukraine d Institute of Mathematics, University of Rzeszów, Rejtana 16 A, 35-310 Rzeszów, Poland |
| Abstract: | Our main result states that the hyperspace of convex compact subsets of a compact convex subset X in a locally convex space is an absolute retract if and only if X is an absolute retract of weight ?ω1. It is also proved that the hyperspace of convex compact subsets of the Tychonov cube Iω1 is homeomorphic to Iω1. An analogous result is also proved for the cone over Iω1. Our proofs are based on analysis of maps of hyperspaces of compact convex subsets, in particular, selection theorems for such maps are proved. |
| Keywords: | 54B20 54C55 46A55 |
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