This article is cited in 1 paper

Three-Dimensional Spaces Where All Bounded Chebyshev Sets Are Monotone Path Connected

B. B. Bednov<sup>ab

a</sup> I. M. Sechenov First Moscow State Medical University
^b Bauman Moscow State Technical University

Abstract: In a three-dimensional normed space $X$, any bounded Chebyshev set is monotone path connected if and only if one of the following two conditions holds: (1) the set of extreme points of the sphere in the dual space is dense in this sphere; (2) $X=Y\oplus_\infty \mathbb R$ (i.e., the unit sphere of $X$ is a cylinder).

Keywords: Chebyshev set, monotone path connected set, bounded Chebyshev set.

UDC: 517.982.256+517.982.252

Received: 29.04.2022
Revised: 09.01.2023

DOI: 10.4213/mzm13569

 English version: Mathematical Notes, 2023, 114:3, 283–295

Bibliographic databases:

• 
•