Abstract
AbstractIt is shown that a normed linear space admitting (Chebyshev) centers is complete. Then the ideas in the proof of this fact are used to show that every incomplete CLUR (compactly locally uniformly rotund) normed linear space contains a closed bounded convex subset B with the following properties: (a)Bdoes not contain any farthest point; (b)Bdoes not contain any nearest point (to the elements of its complement).
Publisher
Cambridge University Press (CUP)
Subject
General Mathematics,Statistics and Probability
Cited by
1 articles.
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1. Inscribed centers, reflexivity, and some applications;Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics;1986-12