This article is cited in 4 papers

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

B. B. Bednov<sup>abc

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

Abstract: 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.

Keywords: Chebyshev set, convexity, monotone path-connectedness, smoothness.

UDC: 517.982.256+517.982.252

Received: 30.09.2021
Revised: 17.11.2021

DOI: 10.4213/mzm13314

 English version: Mathematical Notes, 2022, 111:4, 505–514

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