Geometric construction of Chebyshev sets and suns in three-dimensional spaces with cylindrical norm
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2020), pp. 26-32
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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.
@article{VMUMM_2020_5_a3,
author = {A. R. Alimov},
title = {Geometric construction of {Chebyshev} sets and suns in three-dimensional spaces with cylindrical norm},
journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
pages = {26--32},
publisher = {mathdoc},
number = {5},
year = {2020},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VMUMM_2020_5_a3/}
}
TY - JOUR AU - A. R. Alimov TI - Geometric construction of Chebyshev sets and suns in three-dimensional spaces with cylindrical norm JO - Vestnik Moskovskogo universiteta. Matematika, mehanika PY - 2020 SP - 26 EP - 32 IS - 5 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/VMUMM_2020_5_a3/ LA - ru ID - VMUMM_2020_5_a3 ER -
%0 Journal Article %A A. R. Alimov %T Geometric construction of Chebyshev sets and suns in three-dimensional spaces with cylindrical norm %J Vestnik Moskovskogo universiteta. Matematika, mehanika %D 2020 %P 26-32 %N 5 %I mathdoc %U http://geodesic.mathdoc.fr/item/VMUMM_2020_5_a3/ %G ru %F VMUMM_2020_5_a3
A. R. Alimov. Geometric construction of Chebyshev sets and suns in three-dimensional spaces with cylindrical norm. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2020), pp. 26-32. http://geodesic.mathdoc.fr/item/VMUMM_2020_5_a3/