## Taiwanese Journal of Mathematics

### REMOTAL SETS REVISITED

#### 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.

#### Article information

Source
Taiwanese J. Math., Volume 5, Number 2 (2001), 367-373.

Dates
First available in Project Euclid: 18 July 2017

https://projecteuclid.org/euclid.twjm/1500407343

Digital Object Identifier
doi:10.11650/twjm/1500407343

Mathematical Reviews number (MathSciNet)
MR1832174

Zentralblatt MATH identifier
1030.46018

#### Citation

Baronti, Marco; Papini, Pier Luigi. REMOTAL SETS REVISITED. Taiwanese J. Math. 5 (2001), no. 2, 367--373. doi:10.11650/twjm/1500407343. https://projecteuclid.org/euclid.twjm/1500407343