函数连续与导数的分析

Discussion of Function Continuity and Derivative

本文讨论了函数可导与导函数的连续性的联系，阐述了函数在一点连续与在该点的任意邻域内连续的关系以及函数在一点可导与在该点的任意邻域内可导的关系。

This paper discussed the relation between the derivable property of functions and the continuity of derived function in detail. The paper also expounded the relation between functional continuity at the point Xo and functional discontinuous point in proximity space of the point Xo, the relation between functional continuity at the point xo and functional continuity in proximity space of the point xo, and the relation between functional derivable property at the point Xo and functional derivable property in proximity space of the point x0.