关于函数介值性与连续性的研究

Discussions on the continuous properly and intermediate value property of function

本文对函数介值性与连续性之间的关系进行了研究和讨论,指出函数连续性只是函数介值性的充分条件而非必要条件,从而说明连续函数介值定理的逆命题并不成立。同时并给出并证明了函数介值性或连续性的几个充分条件。

In this paper, I have made discussions and researches on the relationship between the continuous property and intermediate value property of function, pointed out that the continuous property of function is only the sufficient conditon of the intermediate value property of function and isn't the necessary condition of this theorem, and illustrated the contrary theorem of the intermediate value theorem isn't set up, At the same time ,1 gave out and proved the several sufficient conditions of the intermediate value property or continuous property of f'unction