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2001 REMOTAL SETS REVISITED
Marco Baronti, Pier Luigi Papini
Taiwanese J. Math. 5(2): 367-373 (2001). DOI: 10.11650/twjm/1500407343

Abstract

Farthest point theory is not so rich and developed as nearest point theory, which has more applications. Farthest points are useful in studying the extremal structure of sets; see, e.g., the survey paper [14]. There are some interactions between the two theories; in particular, uniquely remotal sets in Hilbert spaces are related to the old open problem concerning the convexity of Chebyshev sets. The aim of this paper is twofold: first, we indicate characterizations of inner product spaces and of infinite-dimensional Banach spaces, in terms of remotal points and uniquely remotal sets. Second, we try to update the survey paper [15], concerning uniquely remotal sets.

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Marco Baronti. Pier Luigi Papini. "REMOTAL SETS REVISITED." Taiwanese J. Math. 5 (2) 367 - 373, 2001. https://doi.org/10.11650/twjm/1500407343

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Published: 2001
First available in Project Euclid: 18 July 2017

zbMATH: 1030.46018
MathSciNet: MR1832174
Digital Object Identifier: 10.11650/twjm/1500407343

Rights: Copyright © 2001 The Mathematical Society of the Republic of China

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Vol.5 • No. 2 • 2001
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