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Matematicheskie Zametki, 2022, Volume 111, Issue 4, Pages 483–493
DOI: https://doi.org/10.4213/mzm13314 (Mi mzm13314) 		 
This article is cited in 4 scientific papers (total 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. Bednovabc

a Lomonosov Moscow State University
b Bauman Moscow State Technical University
c I. M. Sechenov First Moscow State Medical University
Full-text PDF (471 kB) Citations (4)
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DOI: https://doi.org/10.4213/mzm13314
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.
Funding agency Grant number
Russian Science Foundation 22-21-00415
This work was supported by the Russian Science Foundation under grant no. 22-21-00415.
Received: 30.09.2021
Revised: 17.11.2021
English version:
Mathematical Notes, 2022, Volume 111, Issue 4, Pages 505–514
DOI: https://doi.org/10.1134/S000143462203018X
Bibliographic databases:
Document Type: Article
UDC: 517.982.256+517.982.252
Language: Russian
Citation: B. B. Bednov, “Finite-Dimensional Spaces where the Class of Chebyshev Sets Coincides with the Class of Closed and Monotone Path-Connected Sets”, Mat. Zametki, 111:4 (2022), 483–493; Math. Notes, 111:4 (2022), 505–514
Citation in format AMSBIB
\Bibitem{Bed22}
\by B.~B.~Bednov
\paper Finite-Dimensional Spaces where the Class of Chebyshev Sets Coincides with the Class of Closed and Monotone Path-Connected Sets
\jour Mat. Zametki
\yr 2022
\vol 111
\issue 4
\pages 483--493
\mathnet{http://mi.mathnet.ru/mzm13314}
\crossref{https://doi.org/10.4213/mzm13314}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4461278}
\transl
\jour Math. Notes
\yr 2022
\vol 111
\issue 4
\pages 505--514
\crossref{https://doi.org/10.1134/S000143462203018X}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85128936072}
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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