连续函数的非极值点和单调区间

Non-Extreme Points and Monotonic Intervals of Continuous Functions

本文证明了非常数连续函数的非极值点的全体有连续基数,讨论了无常数区间的连续函数存在单调区间的充分必要条件.

Let f be a real -valued continuous function which is non-constact in any subinterval of the domain. In this paper, we prove that the complement of all local maximum and minimun points is a continuum.Furthermore,a necessary and sufficient condition for f being monoton-ic in some subinterval is given.