平面上同分母有理点的稠密性及其应用  

The Density of Rational Points with the Same Denominators on the Plane and its Application

作　　者：杨智强 王仙桃 YANG Zhi-qiang;WANG Xian-tao(Department of Mathematics,College of Science,Shantou University,Shantou Guangdong 515063,China)

机构地区：[1]汕头大学理学院数学系,广东汕头515063

出　　处：《大学数学》2018年第1期123-126,共4页College Mathematics

基　　金：国家自然科学基金(11571216);汕头大学引进教师科研启动经费项目

摘　　要：证明了实平面上同分母有理点集的稠密性.作为此结果的应用,构造了实平面上的一个简单函数,此函数说明实平面上具有稠密不连续点集的Riemann可积函数是存在的.The aim of this paper is twofold.The first aim is to prove the density of a class of rational points(i.e.,their coordinates are rational)in R2,where the denominators of the coordinates of every such point are prime and the same.The second one,as an application of the obtained density,is to construct a simple function in R2 such that it is Riemann integrable and the set of its discontinuities is dense.

关 键 词：稠密性 同分母有理点 RIEMANN函数 

分 类 号：O172.2[理学—数学]