This article is cited in 17 papers

Almost convex and Chebyshev sets

L. I. Vlasov

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

Abstract: Properties of normed spaces in which every almost convex set is convex are derived. In such spaces every Chebyshev set with a continuous metric projection is convex.

UDC: 517.5

Received: 20.01.1969

 English version: Mathematical Notes, 1970, 8:5, 776–779

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