子集系统决定的拓扑空间  

On topological spaces determined by subset systems

作　　者：陈耀 徐晓泉[1] CHEN Yao;XU Xiao-quan(College of Mathematics and Information Science,Jiangxi Normal University,Nanchang 330022,China)

机构地区：[1]江西师范大学数学与信息科学学院

出　　处：《高校应用数学学报（A辑）》2019年第4期487-491,共5页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(11661057);“赣鄱英才555工程”科技领军人才培养计划;江西省自然科学基金(20161BAB2061004)

摘　　要：对子集系统Z,引入了由Z所诱导的算子dZ,讨论了由子集系统决定的拓扑空间,主要结果如下:(1)单点子集系统和有限子集系统决定的拓扑相同;(2)对于单点,有限,幂集和链四种子集系统Z, dZ是拓扑算子,且dZ2=dZ,从而对任意T0的拓扑空间(X,τ), dZ(τ)是细于τ的最粗的ZD拓扑.For a subset system Z, the induced operator dZ is introduced, and the topological spaces determined by Z are discussed. The main results are:(1) the topological spaces determined by the single point subset system are the same with the ones determined the finite subset system;(2) if Z is one of the single subset system, the finite subset system, the power subset system and the chain system, then dZ is a topological operator and dZ2= dZ. Therefore, for each T0 space(X, τ), dZ(τ)) is the coarsest ZD topology which is finer than τ.

关 键 词：子集系统Z 诱导算子d_Z ZD空间 

分 类 号：O189.1[理学—数学]