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.
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)
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)
关键词
有理数集
稠密性
可分性
介值性
导集
rational numbers
density
separability
the property of intermediate value
derived set
