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Matematicheskie Zametki, 2023, Volume 114, Issue 3, Pages 323–338
DOI: https://doi.org/10.4213/mzm13569 (Mi mzm13569) 		 
This article is cited in 1 scientific paper (total in 1 paper)

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

B. B. Bednovab

a I. M. Sechenov First Moscow State Medical University
b Bauman Moscow State Technical University
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DOI: https://doi.org/10.4213/mzm13569
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.
Funding agency Grant number
Russian Science Foundation 22-21-00415
This work was financially supported by the Russian Science Foundation, project 22-21-00415, https://rscf.ru/en/project/22-21-00415/.
Received: 29.04.2022
Revised: 09.01.2023
English version:
Mathematical Notes, 2023, Volume 114, Issue 3, Pages 283–295
DOI: https://doi.org/10.1134/S0001434623090018
Bibliographic databases:
Document Type: Article
UDC: 517.982.256+517.982.252
Language: Russian
Citation: B. B. Bednov, “Three-Dimensional Spaces Where All Bounded Chebyshev Sets Are Monotone Path Connected”, Mat. Zametki, 114:3 (2023), 323–338; Math. Notes, 114:3 (2023), 283–295
Citation in format AMSBIB
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\by B.~B.~Bednov
\paper Three-Dimensional Spaces Where All Bounded Chebyshev Sets Are Monotone Path Connected
\jour Mat. Zametki
\yr 2023
\vol 114
\issue 3
\pages 323--338
\mathnet{http://mi.mathnet.ru/mzm13569}
\crossref{https://doi.org/10.4213/mzm13569}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4658781}
\transl
\jour Math. Notes
\yr 2023
\vol 114
\issue 3
\pages 283--295
\crossref{https://doi.org/10.1134/S0001434623090018}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85174710189}
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    • This publication is cited in the following 1 articles:
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