序半群上的S-拓扑  

S-topology on Ordered Semigroups

作　　者：夏常春 赵彬[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

出　　处：《模糊系统与数学》2015年第4期1-5,共5页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(11171196;11301316);中央高校基本科研业务费专项基金资助项目(GK201302003)

摘　　要：引入了序半群上S-拓扑和强S-拓扑的概念,给出了S-闭集和强S-闭集的等价刻画,讨论了序半群赋上强S-拓扑的连续映射和序半群同态的关系,最后证明了S-拓扑的闭集格关于包含序构成一个代数的完全分配格。In this paper, the notions of S-topology and strongly S-topology on ordered semigroups are proposed, and equivalent characterizations of S-closed subset and strongly S-closed subset are given. The relation between continuous mapping of strongly S-topological spaces and homomorphism of ordered semigroups is discussed, and it is proved that the family of all S-closed sets forms an algebraic and completely distributive lattice under the set-inclusion order.

关 键 词：序半群 S-拓扑 S-闭集 S-开集 

分 类 号：O152[理学—数学]