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.
出处
《数学年刊（A辑）》
CSCD
北大核心
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.
关键词
二元关系
正则性
拓扑
完全正则性
Binary relation, Regularity, Topology, Complete regularity
