完备格上预余拓扑的确定  

Determination of pre-cotopologies on a complete lattice

作　　者：李娜[1,2] 李生刚[1] 苏华飞[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710062 [2]西安外事学院经济管理学院,陕西西安710077

出　　处：《纺织高校基础科学学报》2008年第4期429-434,共6页Basic Sciences Journal of Textile Universities

基　　金：国家自然科学基金资助项目(10271069)

摘　　要：通过定义完备格L上的预余拓扑、预闭包算子、预外导算子族、预内部算子、覆盖族及它们上的序关系,研究给定完备格L上预余拓扑的确定方式.证明了(1)给定完备格L上预余拓扑的全体、预闭包算子的全体构成了彼此同构的完备格;(2)当L是闭集格时,L上预外导算子族的全体与预余拓扑的全体构成了彼此同构的完备格;(3)当L是完备DeMorgan代数时,L上的预余拓扑的全体、预内部算子的全体、覆盖族的全体构成了彼此同构的完备格.因此给定完备格L上的预余拓扑可以由L上的预闭包算子、预外导算子族、预内部算子及覆盖族确定.The notions of pre-cotopology, pre-closure operator, family of pre-outside-derived operators, pre-interior operator, family of covers, and their orders on a given complete lattice are introduced, and the way to determine pre-cotopologies on a complete lattice is studied. It is proved that, for a given com- plete lattice L, （1） Both （CT（L） ,C） （the set of all pre-cotopologies on L） and （CL（L）, ≤） （the set of all pre-closure operators on L） are complete lattices which are isomorphic each other. （2） If L is a closed- set lattice, then both （CT（L） ,C） and （FD（L）, ≤） （the set of all families of pre-outside-derived operators on L） are complete lattices which are isomorphic each other. （3） If L is a complete DeMorgan algebra, then both （IN（L）, ≤） （the set of all pre-interior operators） and （FC（L）, ≤） （the set of all families of covers on L） are complete lattices which are isomorphic with （CT（L）,C）. Thus a pre-cotopology on a given complete lattice may be determininated by a pre-closure operator, a family of pre-outside-derived operators, a pre-interior operator, or a family of covers.

关 键 词：预余拓扑 预闭包算子 预外导算子族 预内部算子 覆盖族 

分 类 号：O189.1[理学—数学]