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Mat. Zametki, 2015, Volume 97, Issue 1, Pages 142–149 (Mi mz10462)  

This article is cited in 1 scientific paper (total in 1 paper)

Locally Chebyshev Sets on the Plane

A. A. Flerov

M. V. Lomonosov Moscow State University

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).


DOI: https://doi.org/10.4213/mzm10462

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English version:
Mathematical Notes, 2015, 97:1, 136–142

Bibliographic databases:

Document Type: Article
UDC: 517.982.256
Received: 03.03.2014
Revised: 13.06.2014

Citation: A. A. Flerov, “Locally Chebyshev Sets on the Plane”, Mat. Zametki, 97:1 (2015), 142–149; Math. Notes, 97:1 (2015), 136–142

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Alimov A.R., “On Approximative Properties of Locally Chebyshev Sets”, Proc. Inst. Math. Mech., 44:1 (2018), 36–42  isi
  • Математические заметки Mathematical Notes
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