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On convex bodies of constant width |
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| Authors: | L.E. Bazylevych |
| Affiliation: | a National University “Lviv Polytechnica”, 12 Bandery Str., 79013 Lviv, Ukraine b Lviv National University, 1 Universytetska Str., 79000 Lviv, Ukraine c Institute of Mathematics, University of Rzeszów, 16A Rejtana Str., 35-310 Rzeszów, Poland |
| Abstract: | We present an alternative proof of the following fact: the hyperspace of compact closed subsets of constant width in Rn is a contractible Hilbert cube manifold. The proof also works for certain subspaces of compact convex sets of constant width as well as for the pairs of compact convex sets of constant relative width. Besides, it is proved that the projection map of compact closed subsets of constant width is not 0-soft in the sense of Shchepin, in particular, is not open. |
| Keywords: | 54B20 52A20 46A55 |
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