从超实数域R到R内的函数的两种连续性 　　  

Two kinds of continuity of functions from hyperreal number field *R into *R

作　　者：张福泰[1] 冯汉桥 

机构地区：[1]陕西师范大学计算机科学系

出　　处：《陕西师大学报（自然科学版）》1996年第1期16-20,共5页Journal of Shaanxi Normal University(Natural Science Edition)

基　　金：陕西师范大学青年科学基金

摘　　要：用非标准分析的方法，讨论了从超实数域＊Ｒ到＊Ｒ内的函数的两种连续性——Ｑ－连续性与Ｓ－连续性．给出了这两种连续函数的一些基本性质以及它们与通常的实连续函数之间的关系，并证明了超实数域内闭区间上的这两类连续函数具有与实数域内闭区间上的连续函数相类似的一些性质．Non standard methods are used to study two kinds of continuity, that is Q con tinuity and S continuity of functions from the field *R into *R corresponding to Q topology and S topology on *R respectively. Some basic properties of them are established. Especially, it is proved that these two kinds of functions on closed intervals within * R have properties similar to those of real valued continuous functions on closed intervals within R. Some mistakes of a foreign scholar about Q continuity are corrected as well.

关 键 词：非标准分析 超实数域 Q-连续 S-连续 连续函数 

分 类 号：O141.41[理学—数学]