L-拟序集上的广义Alexandroff拓扑  

Generalized Alexandroff Topologies on L-Quasi Ordered Sets

作　　者：张奇业[1] 郑崇友[1] 

机构地区：[1]首都师范大学数学系,北京100037

出　　处：《模糊系统与数学》2002年第1期13-17,共5页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目 (199710 5 9)

摘　　要：在一类特殊的 L -拟序集上定义广义 Alexandroff拓扑 ,限制到通常的拟序集上就是 Alexandroff拓扑 ,并且该拓扑可以由其上的一族 Alexandroff拓扑取并得到。还证明任意一个拓扑空间的拓扑都可以表示为某个 L-拟序集上的广义 Alexandroff拓扑。In this paper,the generalized Alexandroff topology on an L-quasi ordered set is constructed, where L denotes a completely distributive lattice in which 1 is a molecule, it is exactly an Alexandroff topology when restricted to the ordinary quasi ordered set.It is proved that the generalized Alexandroff topology on an L-quasi ordered set (X,e) can be obtained by the join of a family of the Alexandroff topologies on X, and a topology on any topological space can be represented as a generalized Alexandroff topology on an L-quasi ordered set.

关 键 词：拓扑 拟序集 L-单调映射 广义Alexandroff拓扑 完全分配格 DOMAIN理论 

分 类 号：O189.13[理学—数学]