从连续到间断——关于介值定理的推广

From Continuous to Discontinuous,a Generalization of Intermediate Value Theorem

单变量连续函数已经被研究了近300年,很难想象其中还有未被开恳的处女地.本文将连续函数的介值定理推广到间断的情况,文中的思想方法在其他领域如数论中也是有用的.

Continuous function of a single variable has been studied for all most 300 years. It is hard to believe that in such a field there is still some virgin land. In this paper, we generalize the intermediate value theorem from continuous to discontinuous. The method used here is also useful in other field like number theory.