C^k(M)类函数集列紧的充要条件  

Sufficient and Necessary Condition of SequentialCompactness of Sets of C^k(M)-Class Functions

作　　者：周继东[1] 董祖引[1] 

机构地区：[1]河海大学数理系,南京210098

出　　处：《数学的实践与认识》2002年第4期669-672,共4页Mathematics in Practice and Theory

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.

关 键 词：C^k(M)类函数集列紧 充要条件 完全有界集 等度连续 

分 类 号：O174.1[理学—数学]