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Matematicheskie Zametki, 2015, Volume 97, Issue 1, Pages 142–149
DOI: https://doi.org/10.4213/mzm10462 (Mi mzm10462) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Locally Chebyshev Sets on the Plane

A. A. Flerov

M. V. Lomonosov Moscow State University
Full-text PDF (439 kB) Citations (6)
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DOI: https://doi.org/10.4213/mzm10462
Abstract: The notion of locally Chebyshev set is introduced and the relationship between Chebyshev and locally Chebyshev sets on the plane is studied. It is shown that any connected closed locally Chebyshev set in an arbitrary Banach space is a Chebyshev set and each Chebyshev set is locally Chebyshev if and only if the space is strictly convex.
Keywords: Chebyshev set, locally Chebyshev set, metric projection, Banach space.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation НШ-3682.2014.1
This work was supported by the program ``Leading Scientific Schools'' (grant no. NSh-3682.2014.1).
Received: 03.03.2014
Revised: 13.06.2014
English version:
Mathematical Notes, 2015, Volume 97, Issue 1, Pages 136–142
DOI: https://doi.org/10.1134/S0001434615010150
Bibliographic databases:
Document Type: Article
UDC: 517.982.256
Language: Russian
Citation: A. A. Flerov, “Locally Chebyshev Sets on the Plane”, Mat. Zametki, 97:1 (2015), 142–149; Math. Notes, 97:1 (2015), 136–142
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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