| 关于赋范线性空间中Chebyshev中心的存在性 |
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| 引用本文： | 倪仁兴.关于赋范线性空间中Chebyshev中心的存在性[J].厦门大学学报(自然科学版),2001,40(1):12-16. |
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| 作者姓名： | 倪仁兴 |
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| 作者单位： | 绍兴文理学院数学系, |
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| 基金项目： | 国家自然科学基金资助项目(19971013)` |
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| 摘 要： | 讨论了空间的完备性与有中心的赋范线性空间的关系，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CLUR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。
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| 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 |
| 文章编号： | 0438-0479(2001)01-0012-05 |
| 修稿时间： | 2000年6月6日 |
On the Existence of Chebyshev Centers in Normed Linear Spaces |
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| NI Ren,xing.On the Existence of Chebyshev Centers in Normed Linear Spaces[J].Journal of Xiamen University(Natural Science),2001,40(1):12-16. |
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| Authors: | NI Ren xing |
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| Abstract: | 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. |
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| Keywords: | incomplete normed linear space compactly locally uniform round spaces maximizing (minimizing) sequence Chebyshev center |
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