一元函数一致连续性的性质

Properties of the Uniformly Continuous Functions with One Variable

首先介绍了一元函数一致连续性的定义和两个充分条件:Cantor定理和Lipschitz判定,其次,给出了连续的周期函数一定是一致连续的,开区间上一致连续函数的延拓刻画,以及两个一致连续函数的线性叠加或复合运算之后仍为一致连续的等若干结论.

The concept of uniformly continuous function,Cantor theorem and Lipschitz criterion which are two sufficient conditions for uniformly continuous function are introduced. Then,the uniform continuity of continuous periodic function is proposed,the extension of uniformly continuous function on open interval is established,and it is obtained that the linear superposition or composition of two uniformly continuous functions is still uniformly continuous as well as other several conclusions.