Monotone path-connectedness of Chebyshev sets in three-dimensional spaces

被引：0
|
作者：
Alimov, A. R. [1 ,2 ,3 ]
Bednov, B. B. [1 ,4 ,5 ]
机构：
[1] Lomonosov Moscow State Univ, Fac Mech & Math, Moscow, Russia
[2] Russian Acad Sci, Steklov Math Inst, Moscow, Russia
[3] Moscow Ctr Fundamental & Appl Math, Moscow, Russia
[4] Bauman Moscow State Tech Univ, Moscow, Russia
[5] IM Sechenov First Moscow State Med Univ, Moscow, Russia
来源：
SBORNIK MATHEMATICS | 2021年 / 212卷 / 05期
关键词：
Chebyshev set; sun; monotone path-connected set; cylindrical norm; CONVEXITY; SUNS;
D O I：
10.1070/SM9325
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We characterize the three-dimensional Banach spaces in which any Chebyshev set is monotone path-connected. Namely, we show that in a three-dimensional space X each Chebyshev set is monotone pathconnected if and only if one of the following two conditions is satisfied: any exposed point of the unit sphere of X is a smooth point or X = Y circle plus(infinity) R (that is, the unit sphere of X is a cylinder).
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页码：636 / 654
页数：19
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