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.
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Original Russian Text © A. A. Flerov, 2015, published in Matematicheskie Zametki, 2015, Vol. 97, No. 1, pp. 139–146.
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Flerov, A.A. Locally Chebyshev sets on the plane. Math Notes 97, 136–142 (2015). https://doi.org/10.1134/S0001434615010150
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DOI: https://doi.org/10.1134/S0001434615010150