紧度量空间连续函数族的可分性 |
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引用本文: | 蔡宇泽.紧度量空间连续函数族的可分性[J].无锡职业技术学院学报,2008,7(6):52-53. |
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作者姓名: | 蔡宇泽 |
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作者单位: | 沙洲职业工业学院,基础科学系,江苏,张家港,215600 |
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摘 要: | 文章讨论了一类紧致度量空间的连续函数的可分性.设为非空度量空间,为其上连续函数组成的集类,我们利用Stone-Weierstrass定理证明了:是可分空间当且仅当是紧致的。
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关 键 词: | 紧集 可分空间 可分点 |
The Separateness of the Family of the Continue Function on a Compact Metric Space |
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Authors: | CAI Yu-ze |
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Institution: | CAI Yu - ze (Shazhou Professional Institute of Technology, Zhangjiagang 215600, China) |
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Abstract: | In the paper,the author discusses the separateness of continuous functions on a compact metric space.Let be a nonempty metric space and be the family of continues functions on it.We apply the Stone-Weierstrass Theorem to prove that is separate iff.is compact. |
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Keywords: | compact set separate space separate point |
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