On existence of farthest points
type: Item
instance of: scholarly article
title: On existence of farthest points
zbMATH Open document ID: 0584.46008
author: B. B. Panda
author: K. Dwivedi
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 1985-01-01T00:00:00Z
review text: Let K be a subset of a Banach space X with the property that every maximising sequence in K has a subsequence weakly converging to some element of K. Then the set \(\{x\in X:\| x-z\| =\sup_{y\in K}\| x-y\|\) for some \(z\in K\}\) contains a dense \(G_{\delta}\)-subset of X. This is an extension of a result of \textit{Ka Sing Lau} in Isr. J. Math. 22, 168-174 (1975; Zbl 0325.46022). Further, if X also satisfies Efimov Stechkin property, then the author shows that the above result is also valid for a set K which is simply closed and bounded.
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 46A55
Mathematics Subject Classification ID: 41A65
zbMATH DE Number: 3935725
zbMATH Keywords: farthest points
zbMATH Keywords: remotal set
zbMATH Keywords: maximising sequence
zbMATH Keywords: Efimov Stechkin property
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3935725