无穷区间上全连续函数及其性质探讨

摘要

提出了无穷区间上全连续函数的概念，并主要用紧区间逼近及举反例的方法成功讨论了其性质，打破了全连续函数在区间[a，b]上的局限性。%This paper advances the notion of completely continuous function that is defined on infinite interval, and more, we successfully discuss its properties mainly using the methods of approximating by compact interval and giving counterexample, which breaks the boundedness of completely continuous function that is defined on finite interval.