正则关系与完全正则空间  

Regular Relations and Completely Regular Spaces

作　　者：徐晓泉[1] 刘应明[2] 

机构地区：[1]江西师范大学数学与信息科学学院,南昌330022 [2]四川大学长江数学中心,成都610064

出　　处：《数学年刊（A辑）》2008年第6期819-828,共10页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.10331010;No.10861007);973(No.2002CB312206);高等学校全国优秀博士学位论文作者专项基金(No.2007B14);教育部博士点基金(No.0020105102019);江西省自然科学基金(No.0411025;No.2007GZS0179);江西师范大学博士基金资助的项目.

摘　　要：借助于关系的某些代数性质刻画拓扑空间的完全正则性,证明了拓扑空间是完全正则的当且仅当其闭集与开集之间存在满足一定简单条件的正则关系,有限正则关系或广义有限正则关系.The main purpose of this paper is to characterize the complete regularity of topological spaces by some algebraic properties of certain binary relations between closed subsets and open subsets. It is proved that a topological space is completely regular if and only if there are certain regular, finitely regular, or generalized finitely regular relations between closed subsets and open subsets.

关 键 词：二元关系 正则性 拓扑 完全正则性 

分 类 号：O189.11[理学—数学]