距离空间上半连续函数的一些性质  

Some Properties of Semi-continuous Functions on a Metric Space

作　　者：郭志华[1] 曹怀信[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,西安710119

出　　处：《渭南师范学院学报》2015年第14期34-39,88,共7页Journal of Weinan Normal University

基　　金：中央高校基本业务费专项资金项目:基于算子理论的多体量子关联分类及其动力学性质研究(GK201402005)

摘　　要：在距离空间上函数的上半连续性与下半连续性有几种不同的刻画,特别是Dirichlet函数在任一有理点处上半连续,在任一无理点处下半连续;Riemann函数在有理点处上半连续但不下半连续;取整函数在任一点处上半连续.同时,在紧致距离空间上,上半连续函数必有最大值,下半连续函数必有最小值.There are several different characterizations of upper semi-continuity and lower semi continuity of functions on a metric space. Especially, the Dirichlet function lies in the upper semi-continuity at any rational point and lower semi-continuity at any irrational point; Riemann function is in the upper semi-continuity at any rational point but not the lower semi continuity ; the in- tegral function is in the upper semi-continuity at any point. At the same time, on a compact metric space, every upper semi-contin- uous function has its maximum value and every lower semi-continuous function has its minimum value.

关 键 词：距离空间 函数 上半连续性 下半连续性 

分 类 号：O177.1[理学—数学]