Z-连续偏序集的特征与稠密度  

Character and Density on Z-Continuous Posets

作　　者：姚丽娟[1] 徐晓泉[1] 

机构地区：[1]江西师范大学数学与信息科学学院,江西南昌330022

出　　处：《江西师范大学学报（自然科学版）》2008年第3期296-299,共4页Journal of Jiangxi Normal University(Natural Science Edition)

基　　金：国家自然科学基金(10331010);江西省自然科学基金(0411025);江西师范大学博士基金资助项目

摘　　要：该文引入了Z-连续偏序集的局部基和稠密子集的概念,基于此定义了Z-连续偏序集的特征和稠密度;给出了局部基的刻画,并讨论了Z-连续偏序集的特征和稠密度与Z-连续偏序集上Z-Scott拓扑和Z-Lawson拓扑的特征、稠密度之间的关系;证明了Z-连续偏序集上Z-Scott拓扑的特征小于或等于Z-连续偏序集及其Z-Lawson拓扑的特征,Z-连续偏序集的稠密度与其Z-Scott拓扑的稠密度相等,且小于或等于Z-Lawson拓扑的稠密度.In this paper, the concepts of local basis, dense set, character and density on Z- continuous posets are introduced. The characterizations of local basis are given. Moreover, the relations among the character, the density, the Z- Scott topology and the Z- Lawson topology on Z- continuous posers are discussed. It is showed that the character of a Z- Scott topology on a Z- continuous poset P is less than that of P and that of the Z- Lawson topology on P , and the density of P is equal to that of Z- Scott topology on P and less than that of Z- Lawson tooology on P.

关 键 词：Z-连续偏序集 局部基 特征 稠密度 

分 类 号：O153.1[理学—数学] O189.1[理学—基础数学]