Uniquely Remotal Sets in Banach Spaces

被引：6

作者：

Sababheh, M. ^{[1
]}

Yousef, A. ^{[2
]}

Khalil, R. ^{[2
]}

机构：

[1] Princess Sumaya Univ Technol, Dept Basic Sci, Amman 11941, Jordan

[2] Univ Jordan, Dept Math, Amman 11942, Jordan

来源：

FILOMAT | 2017年 / 31卷 / 09期

关键词：

Uniquely remotal sets; Farthest points; Approximation theory in Banach spaces;

D O I：

10.2298/FIL1709773S

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The study of the continuity of the farthest point mapping for uniquely remotal sets has been used extensively in the literature to prove the singletoness of such sets. In this article, we show that the farthest point mapping is not continuous even if the set is remotal, rather than being uniquely remotal. Consequently, we obtain some generalizations of results concerning the singletoness of remotal sets. In particular, it is proved that a compact set admitting a unique farthest point to its center is a singleton, generalizing the well known result of Klee.

引用

页码：2773 / 2777

页数：5

共 10 条

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