Arzela-Ascoli定理条件的改变和减弱

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

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.