函数一致连续性研究

函数1致连续性研究

摘要

本文通过几个典型的例子对函数1致连续性的概念进行深入分析，然后由康托定理出发讨论函数1致连续性条件，得到几个判别1致连续性的有用结论和方法，由判别函数1致连续性的方法得到证明函数在区间内非1致连续的简便方法，以加深了对函数1致连续性的概念的理解，最后总结1致连续函数的运算性质，包括复合函数的1致连续性及1致连续函数的4则运算，使得对函数1致连续性的内涵有了更全面，更深刻的理解和认识。
关键词：1致连续；函数；非1致连续；康托定理。

The research of Function uniform continuity

ABSTRACT

In this papers, We discuss uniform continuity of functions.The article carries on the thorough analysis through several typical example to the function uniform continuity concept. And then starting from Cantor theorem discussion function consistent continuity conditions. We get some useful conclusion and the method that distinguished the function whether identically continuously. Finally, we summarized the consistent continuous function operation nature. Including the uniform continuity of Composite function and the mathematical operations of consistent continuous function.
Keywords: Uniformly continuous; Function; Non- Uniformly continuous; Cantor theorem.