关于函数在任意区间上一致连续与非一致连续的条件讨论

Discussion on Condition of Uniform and Nonuniform Continuity of a Function in Arbitrary Boundary

一致连续与非一致连续是数学分析中的一个重要的概念.本文从G.康托尔定理出发,清晰的给出在任意区间的函数一致连续的条件,并且讨论非一致连续的简单的判别方法.

There is an important concept in mathematical analysis,nomely uniform continuity and nonuniform continuity.Proceeding from the theorem of G.Cantor,the paper presents conditions of uniform continuity of a function in arbitrary boundary,and discusses the simple distinguish method for nonuniform continuity.