Heine定理及其扩展

Heine Theorem and Its Extension

Heine定理是《数学分析》中的一个重要定理,它是函数极限和数列极限联系的桥梁.因此,可以将Heine定理进行扩展至数列极限以及多元函数极限,并给出扩展定理的应用,这是判定多元函数极限不存在的又一个重要方法.

In this paper,the Heine theorem is extended to the limits of the series and the limits of the multivariate function,three extended theorems are given and the application of the extended theorems is illustrated.