实数集上有限补拓扑空间的研究  

Research on Finite Complementary Topological Space on Real Numbers Set

作　　者：黄瑞 HUANG Rui(School of Mathematics and Statistics,Fuyang Normal University,236037,Fuyang,Anhui,China)

机构地区：[1]阜阳师范大学数学与统计学院,安徽阜阳236037

出　　处：《淮北师范大学学报（自然科学版）》2021年第4期18-22,共5页Journal of Huaibei Normal University：Natural Sciences

基　　金：安徽省高等学校自然科学研究重点项目(KJ2017A341,KJ2018A0330);安徽省教学研究重大项目(2018jyxm0491);安徽省大规模在线开放课程(2019mooc205);高校优秀拔尖人才培育资助项目(gxgnfx2018017)。

摘　　要：通过对有限补空间ℝ的子空间、道路和收敛序列等问题的讨论,文章研究有限补空间ℝ的连通性、可数性公理、分离性公理和紧性,同时给出什么样的子集是有限补空间ℝ中的连通子集、道路连通子集、局部道路连通子集和紧致子集.Based uponthe discussion on the subspace,the path and convergent sequences of finite complementary spaceon real numbers set,this paper has probed into the connectivity,countability axioms,separation axioms and compactness which the finite complementary spaceon real numbers set satisfies,and the paper also shows what kind of subset is the connected subset,path connected subset,local path connected subset and compact subset in the finite complementary spaceon real numbers set.

关 键 词：有限补空间ℝ 连通性 可数性公理 分离性公理 紧性 

分 类 号：O189.11[理学—数学]