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Plane Sets That are Chebyshev in Some Norm

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Abstract

Plane sets each of which is Chebyshev in some norm are described in the paper.

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REFERENCES

  1. A. R. Alimov and I. G. Tsarkov, Geometric Approximation Theory, Part I: Classical Concepts and Constructions of Approximations by Sets (OntoPrint, Moscow, 2017).

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  2. R. L. Moore, ‘‘Concerning triods in the plane and the junction points of plane continua,’’ Proc. Natl. Acad. Sci. U. S. A. 14, 85–88 (1928).

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  3. A. R. Alimov, ‘‘The geometric structure of Chebyshev sets in \(l^{\infty}(n)\),’’ Funct. Anal. Its Appl. 39, 1–8 (2005). doi 10.1007/s10688-005-0012-x

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ACKNOWLEDGMENTS

he author thanks P.A. Borodin for problem formulation and O.N. Kosukhin for valuable comments.

Funding

The work is supported by the Theoretical Physics and Mathematics Advancement Foundation ‘‘BASIS’’.

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Authors and Affiliations

  1. Chair of Theory of Functions and Functional Analysis, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia

    K. S. Shklyaev

  2. Laboratory Multivariate Approximation and Applications, Moscow Center for Fundamental and Applied Mathematics, Moscow, Russia

    K. S. Shklyaev

Authors
  1. K. S. Shklyaev
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Corresponding author

Correspondence to K. S. Shklyaev.

Additional information

Translated by E. Oborin

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Cite this article

Shklyaev, K.S. Plane Sets That are Chebyshev in Some Norm. Moscow Univ. Math. Bull. 76, 69–72 (2021). https://doi.org/10.3103/S0027132221020066

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  • DOI: https://doi.org/10.3103/S0027132221020066

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