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Chebyshev sets and some generalizations of them

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Abstract

In this note we generalize and strengthen certain results contained in [12]. For example, we establish that, in a uniformly convex and smooth Banach space, any locally compact Chebyshev set is convex.

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Authors and Affiliations

  1. Sverdlovsk Section, V. A. Steklov Mathematics Institute, Academy of Sciences of the USSR, USSR

    L. P. Vlasov

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  1. L. P. Vlasov
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Additional information

Translated from Matematicheskie Zametki, Vol. 3, No. 1, pp. 59–69, January, 1968.

I wish to express my thanks to S. B. Stechkin for his valuable comments.

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Vlasov, L.P. Chebyshev sets and some generalizations of them. Mathematical Notes of the Academy of Sciences of the USSR 3, 36–41 (1968). https://doi.org/10.1007/BF01386963

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