有理数集的可数性与稠密性应用  

Applications of Countability and Density of Rational Numbers

作　　者：祁瑞生 徐大树 QI Ruisheng;XU Dashu(School of Mathematics and Statistic,North-Eastern University at Qin Huangdao,Qin Huangdao 066000, China)

机构地区：[1]东北大学秦皇岛分校数学与统计学院

出　　处：《安庆师范大学学报（自然科学版）》2019年第3期105-108,共4页Journal of Anqing Normal University(Natural Science Edition)

基　　金：国家青年自然科学基金(11701073)

摘　　要：有理数集是可数集且在实数集中稠密,这导致实数集在欧氏度量下成为可分的度量空间。本文从有理数集的这两个特点出发,分别总结了它们在初等数学、数学分析、拓扑学以及泛函分析中广泛而重要的应用。The set of all rational numbers is countable and dense in the real number field which makes the real number field be a separable set. In this paper, we study the applications in the field of elementary mathematics,mathematical analysis, topology and functional analysis based on the properties of rational numbers.

关 键 词：有理数集 稠密性 可分性 介值性 导集 

分 类 号：O171[理学—数学]