Chebyshev sets

Authors

James Fletcher, University of WollongongFollow
W Moors, University of Auckland

RIS ID

96026

Publication Details

Fletcher, J. & Moors, W. B. (2015). Chebyshev sets. Journal of the Australian Mathematical Society, 98 (2), 161-231.

Abstract

A Chebyshev set is a subset of a normed linear space that admits unique best approximations. In the first part of this paper we present some basic results concerning Chebyshev sets. In particular, we investigate properties of the metric projection map, sufficient conditions for a subset of a normed linear space to be a Chebyshev set, and sufficient conditions for a Chebyshev set to be convex. In the second half of the paper we present a construction of a nonconvex Chebyshev subset of an inner product space.