Abstract
Various generalizations of the notion of “sun” are considered and connections among them are established. A series of results from works of the author on Chebyshev sets are restated in new terms. It is proved that a Chebyshev set with a continuous metric projection is convex in a smooth reflexive space.
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Translated from Mathematicheskie Zametki, Vol. 7, No. 5, pp. 593–604, May, 1970.
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Vlasov, L.P. Approximate properties of sets in banach spaces. Mathematical Notes of the Academy of Sciences of the USSR 7, 358–364 (1970). https://doi.org/10.1007/BF01123847
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DOI: https://doi.org/10.1007/BF01123847