This article is cited in 7 papers

Approximate properties of sets in Banach spaces

L. P. Vlasov

Sverdlovsk Branch, V. A. Steklov Mathematical Institute, Academy of Sciences of the USSR

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.

UDC: 517.5

Received: 30.06.1969

 English version: Mathematical Notes, 1970, 7:5, 358–364

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