关于赋范线性空间中Chebyshev中心的存在性  

On the Existence of Chebyshev Centers in Normed Linear Spaces

作　　者：倪仁兴[1] 

机构地区：[1]绍兴文理学院数学系,浙江绍兴312000

出　　处：《厦门大学学报（自然科学版）》2001年第1期12-16,共5页Journal of Xiamen University：Natural Science

基　　金：国家自然科学基金!资助项目 ( 199710 13)

摘　　要：讨论了空间的完备性与有中心的赋范线性空间间的关系 ,用构造性的方法证得了有中心的赋范线性空间必完备 ;完备的赋范线性空间未必有中心 .指出不完备 CL UR赋范线性空间 X总有一有界闭凸子集 B,它既无远达点又对 X\B无最佳逼近点 .The relationship between completeness of spaces and normed linear spaces admitting centers is discussed. By using constructive method, it is proved that a normed linear space admitting centers must be complete and complete normed linear space may not admit center. As a result, it is shown that each imcomplete CLUR normed linear space X contains a closed bounded convex subset B with the following properties: 1) B does not contain any farthest point in X; 2) B does not contain any nearest point to the elements of its complement.

关 键 词：赋范线性范围 紧局部一致凸空间 极大化序列 极小化序列 CHEBYSHEV中心 

分 类 号：O177.2[理学—数学]