This article is cited in 6 papers

Locally Chebyshev Sets on the Plane

A. A. Flerov

M. V. Lomonosov Moscow State University

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.

Keywords: Chebyshev set, locally Chebyshev set, metric projection, Banach space.

UDC: 517.982.256

Received: 03.03.2014
Revised: 13.06.2014

DOI: 10.4213/mzm10462

 English version: Mathematical Notes, 2015, 97:1, 136–142

Bibliographic databases:

• 
• 
• 
• 
•