摘要
通过对数学空间概念二重性的研究,展现了数学空间从欧几里得空间到拓扑空间的发展历程.在19世纪末20世纪初,数学公理化方法迅速发展以及开集概念产生的基础上,讨论了开集与拓扑空间公理体系之间的关系,得出了以开集为背景的拓扑空间概念的普遍性.
Through the research of the duality of the concept of mathematical spaces,this paper shows the development process of the mathematical spaces from Euclidean space to topological space.Based on the rapid development of mathematics axiomatic methods during the late 19 th and early 20 th centuries and the emergence of open sets,the relationship is discussed between open sets and the axiomatic system of topological space.The result reveals that the concept of topological space based on open sets is universal.
出处
《高等数学研究》
2015年第4期8-10,共3页
Studies in College Mathematics
基金
内蒙古师范大学资助项目(2013ZRYB16)
关键词
欧几里得空间
拓扑空间
公理
开集
Euclidean space
topological space
axiom
open set
