从确界原理出发讨论函数的连续性  

Discussion of the continuity of functions according to the principle of exact bounds

作　　者：王秀兰[1] 仲崇斌[1] 潘万富[1] 

机构地区：[1]哈尔滨师范大学恒星学院数学与计算机系,黑龙江哈尔滨150025

出　　处：《高师理科学刊》2007年第2期13-15,共3页Journal of Science of Teachers＇College and University

基　　金：黑龙江省高教学会"十一五"规划项目(115C-580)

摘　　要：以上确界原理为公理,由此公理出发,不必利用区间套定理和有限覆盖定理,直接讨论闭区间上连续函数的几个重要性质及数列极限的柯西准则.这样处理,使得这几个性质的证明自然,通俗易懂,教者易教,学者易学,同时做到提出问题,马上解决问题。Discussed directly some fundamental properties of continuous functions on closed interval and Cauchy criterion on limite of number sequence, need not interval theorem and finitrly covered theorem. This disposal guarantees that the proofs of these properties are easy to understand, teach and learn in the meantime, the problems can be solved as soon as they appear.

关 键 词：确界原理 连续 聚点 

分 类 号：O172[理学—数学]