| C~k(M)类函数集列紧的充要条件 |
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| 引用本文： | 周继东,董祖引. C~k(M)类函数集列紧的充要条件[J]. 数学的实践与认识, 2002, 32(4): 669-672 |
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| 作者姓名： | 周继东 董祖引 |
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| 作者单位： | 河海大学数理系,南京,210098 |
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| 摘 要： | 本文讨论了 Rn中紧集 M上 Ck类函数 ,用构造 ε-网的方法给出了这类函数集列紧的一个充要条件 ,从而推广了著名的 Ascoli-Arzela定理
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| 关 键 词： | 列紧 紧 ε-网 完全有界集 等度连续 |
| 修稿时间： | 1999-04-10 |
Sufficient and Necessary Condition of Sequential Compactness of Sets of Ck(M)-Class Functions |
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| ZHOU Ji-dong,DONG Zu-yin. Sufficient and Necessary Condition of Sequential Compactness of Sets of Ck(M)-Class Functions[J]. Mathematics in Practice and Theory, 2002, 32(4): 669-672 |
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| Authors: | ZHOU Ji-dong DONG Zu-yin |
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| Abstract: | In this paper, We discuss C +k(M)-Class functions on a compact set M in R +n, and by constructing ε-nets, we give a sufficient and necessary condition to the sequential compact set of C +k(M)-Class function, so that extend the well-known Ascoli-Arzela′s Theorem. |
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| Keywords: | sequential compactness compactness ε-net totally bounded set equicontinuity |
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