Arzela-Ascoli定理条件的改变和减弱  

A Change and Reduction of the Condition on Arzela′s Theorem

作　　者：张亚林[1] 

机构地区：[1]天津大学理学院,天津300072

出　　处：《太原师范学院学报（自然科学版）》2012年第1期72-74,90,共4页Journal of Taiyuan Normal University:Natural Science Edition

摘　　要：文章将Arzela-Ascoli定理中的闭区间[α,β]上的连续函数族扩展到无穷紧空间上的连续算子族,给出了无穷紧空间上的连续算子族相对紧性判断的一个充要条件;然后将定理中一致有界减弱为在一点有界,定理的结论仍然成立.The continuous function groups in Arzela-Ascoli theoren which defined on are reduced to a class of continuous operator groups defined on infinity dimension complact spaces,and the sufficient and necessary conditions are given for relative compactncss of a class of continuous operator groups.The uniformly boundedness condition is weakcned to bound in a point,the theorem is still on in this case.

关 键 词：Arzela-Ascoli定理 相对紧 等度连续 一致有界 

分 类 号：O174.1[理学—数学]