Convexity of 2-Chebyshev sets in a Hilbert space. (English. Russian original) Zbl 1212.52002

Borodin, P. A.

Mosc. Univ. Math. Bull. 63, No. 3, 96-98 (2008); translation from Vestn. Mosk. Univ., Ser. I 2008, No. 3, 16-19 (2008).

The author introduces the notion of 2-Chebyshev set in a Banach space. It is proved that, in a Hilbert space, a set is 2-Chebyshev if and only if it is convex and closed.

Reviewer: V. V. Vlasov (Moskva)

MSC:

52A07	Convex sets in topological vector spaces (aspects of convex geometry)
46A55	Convex sets in topological linear spaces; Choquet theory

Keywords:

2-Chebyshev set; convexity in Hilbert space