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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2020, Number 5, Pages 26–32 (Mi vmumm4347)  
This article is cited in 1 scientific paper (total in 1 paper)

Mathematics

Geometric construction of Chebyshev sets and suns in three-dimensional spaces with cylindrical norm

A. R. Alimovab

a Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
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Abstract: A geometric characterization of Chebyshev sets and suns in three-dimensional polyhedral spaces with cylindrical norm is presented. A number of new properties of Chebyshev sets, suns, and sets with continuous metric projection in three-dimensional cylindrical spaces is put forward. The new recent fact due to A. R. Alimov and E. V. Shchepin that suns and Chebyshev sets are convex in tangent directions to the unit sphere plays an important role in the paper.
Key words: Chebyshev set, sun, monotone path-connected set, cylindrical norm, polyhedral norm.
Funding agency Grant number
Russian Foundation for Basic Research 18-01-00333-а
19-01-00332-a
Received: 25.10.2019
English version:
Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 2020, Volume 75, Issue 5, Pages 209–215
DOI: https://doi.org/10.3103/S0027132220050022
Bibliographic databases:
Document Type: Article
UDC: 517.982.256+517.982.252
Language: Russian
Citation: A. R. Alimov, “Geometric construction of Chebyshev sets and suns in three-dimensional spaces with cylindrical norm”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2020, no. 5, 26–32; Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 75:5 (2020), 209–215
Citation in format AMSBIB
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