R^n空间中开集、闭集的新表述及其特点

New Definitions of the Open Set and Closed Set and Their Advantages

避开了《实变函数》、《泛函分析》两门课程中的"所有点全为内点的集为开集,包含所有极限点的集为闭集"这一较抽象的传统定义,给出了一个易于理解,但内容与原定义完全等价的新定义:不含边界点的集称为开集,包含所有边界点的集称为闭集.并通过一些相关定理的证明展示了新定义的优越性.

This paper puts forward new definitions of the open set and closed set, and demonstrates that new definitions are equal to old definitions in meaning and will be ensier to understand. The advantages of new definitions are shown by the demonstration of three related theorems.