单调函数的极限与连续性  

The limit and continuity of monotone function

作　　者：吴智华[1] 

机构地区：[1]朝阳师范高等专科学校,辽宁朝阳122000

出　　处：《辽宁师专学报（自然科学版）》2016年第2期10-11,72,共3页Journal of Liaoning Normal College(Natural Science Edition)

摘　　要：单调函数是一类重要函数,在数学分析解题中经常用到,而关于单调函数的极限存在性、间断点的特点、连续性等内容教材中提到得很少.结合教学实践,对单调函数进行特别研究,证明了单调函数单侧极限的存在性、间断点的跳跃性和可列性以及有限开区间上单调有界连续函数必一致连续等结论.Monotone function is a kind of important function, which is often used in mathematical analysis and problem solving. And on the limit of the existence of the monotone function, the characteristics of discontinuity points, the continuity are seldom mentioned in the textbook. Combining with the teaching practice, the special study on the monotonic function, it proved that the existence of the single side limit of monotone function, the jumping and the countability of the discontinuity point and the monotone bounded continuous function on the finite open interval must be uniformly continuous.

关 键 词：单调函数 极限 间断点 

分 类 号：O171[理学—数学]