Finite-Dimensional Spaces where the Class of Chebyshev Sets Coincides with the Class of Closed and Monotone Path-Connected Sets

被引：3

作者：

Bednov, B. B. ^{[1
,2
,3
]}

机构：

[1] Lomonosov Moscow State Univ, Moscow 119991, Russia

[2] Bauman Moscow Higher Tech Sch Natl Res Univ, Moscow 105005, Russia

[3] Sechenov First Moscow State Med Univ, Moscow 119991, Russia

来源：

MATHEMATICAL NOTES | 2022年 / 111卷 / 3-4期

基金：

俄罗斯科学基金会;

关键词：

Chebyshev set; convexity; monotone path-connectedness; smoothness; CONVEXITY; SUNS;

D O I：

10.1134/S000143462203018X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In a two-dimensional Banach space X, the class of Chebyshev sets coincides with the class of closed and monotone path-connected sets if and only if X is strictly convex. In a finite-dimensional Banach space X of dimension at least 3, this coincidence occurs if and only if X is smooth and strictly convex.

引用

页码：505 / 514

页数：10

共 10 条

[1] Finite-Dimensional Spaces where the Class of Chebyshev Sets Coincides with the Class of Closed and Monotone Path-Connected Sets
B. B. Bednov
Mathematical Notes, 2022, 111 : 505 - 514
[2] Three-Dimensional Spaces Where All Bounded Chebyshev Sets Are Monotone Path Connected
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MATHEMATICAL NOTES, 2023, 114 (3-4) : 283 - 295
[3] Three-Dimensional Spaces Where All Bounded Chebyshev Sets Are Monotone Path Connected
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Mathematical Notes, 2023, 114 : 283 - 295
[4] Properties of monotone path-connected sets
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[5] Monotone path-connectedness of Chebyshev sets in three-dimensional spaces
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Bednov, B. B.
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[6] Convexity of Bounded Chebyshev Sets in Finite-dimensional Asymmetrically Normed Spaces
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IZVESTIYA SARATOVSKOGO UNIVERSITETA NOVAYA SERIYA-MATEMATIKA MEKHANIKA INFORMATIKA, 2014, 14 (04): : 489 - 497
[7] Sets in Rn Monotone Path-Connected with Respect to Some Norm
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[8] Monotone path-connectedness and solarity of Menger-connected sets in Banach spaces
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[9] Solarity and connectedness of sets in the space C[a, b] and in finite-dimensional polyhedral spaces
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[10] Sets in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\boldsymbol{\mathbb{R}^{n}}$$\end{document} Monotone Path-Connected with Respect to Some Norm
E. A. Savinova
Moscow University Mathematics Bulletin, 2023, 78 (1) : 49 - 51

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