英语翻译海涅定理是数学分析课程中重要的定理之一,它是沟通函数极限与数列极限之间的桥梁,它的应用贯穿在数学分析课程乃至高等

Heine theorem is one of the important theorems in mathematical analysis courses. It builds a bridge between function limits and series limits, and its applications emerge through many courses in mathematical analysis or even advanced mathematics. Usually, mathematical analysis textbooks only discuss one general case about Heine theorem, while this paper supplements and proves Heine theorem in the other five cases of function limits, and explores and summarizes the applications of Heine theorem.