On singletonness of uniquely remotal sets
type: Item
instance of: scholarly article
title: On singletonness of uniquely remotal sets
zbMATH Open document ID: 0734.41035
DOI: 10.1007/BF01946377
published in: Periodica Mathematica Hungarica
publication date: 1990-01-01T00:00:00Z
review text: An unsolved problem in approximation theory is: if every point of a normed linear space X admits a unique farthest point in a given bounded set K, then must K be a singleton? In this paper an affirmative answer to the question is given for totally bounded nearly compact sets in complete locally convex linear metric spaces. For earlier work, see \textit{J. Blatter} [Rev. Roum. Math. Pure Appl. 14, 615-621 (1969; Zbl 0205.123)].
Mathematics Subject Classification ID: 41A65
Mathematics Subject Classification ID: 46E40
zbMATH DE Number: 4214656
zbMATH Keywords: farthest point
zbMATH Keywords: singleton
author: T. D. Narang
reviewed by: H. R. Dowson
MaRDI profile type: Publication
cites work: Sets with unique farthest points
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cites work: Nearly compact sets and the farthest point map
description: scientific article; zbMATH DE number 4214656