变动区间上的确界函数是连续函数的证明

Method of Proving Definite Bound Function on Variable Interval as Continuous Function

研究了连续函数在变动区间上的确界函数的连续性问题.通过变动区间与单位区间的对应关系,将变动区间上的确界函数表示为单位区间上的确界函数.利用2个函数的上确界相减的不等式,由函数的一致连续性,证明了变动区间上的确界函数是一致连续的.

We study the continuity of the definite bound function of continuous function on the variable interval.With correspondence between the variable interval and the unit interval,the definite bound function on the change interval is expressed as the definite bound function on the unit interval.With the subtraction inequality of upper bounds of two functions and the uniform continuity of the function,it is proved that the definite bound function is uniformly continuous.