拟连续Domain的特征与浓度  

Character and density of quasicontinuous domains

作　　者：张月玲[1] 汪开云[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：《陕西师范大学学报（自然科学版）》2010年第1期19-22,共4页Journal of Shaanxi Normal University：Natural Science Edition

基　　金：国家自然科学基金资助项目(10871121)

摘　　要：在定向完备偏序集(即Dcpo)上引入局部拟基和稠密子集族的概念,在此基础上定义了拟连续Domain的特征和浓度.利用局部拟基给出拟连续Domain新的等价刻画,并探讨了拟连续Domain的特征、浓度与该拟连续Domain上赋予Scott拓扑或Lawson拓扑时的拓扑空间的特征、浓度之间的关系.证明了拟连续Domain的特征(浓度)等于其上赋予Scott拓扑时的拓扑空间的特征(浓度),且小于等于其上赋予Lawson拓扑时的拓扑空间的特征(浓度).The concepts of local quasi-bases and dense family on directed complete posets are introduced, and the character and density of a quasicontinuous Domain are defined. Using local quasi-bases, a new equivalent characterization of quasicontinuous Domain is obtained. Relations between the character and the density of a quasicontinuous Domain and those on the related spaces with Scott topology or Lawson topology are discussed. It proved that the character and density of a quasicontinuous Domain are respectively equal to those on the related space with Scott topology, but they are respectively less than or equal to those on the related space with Lawson topology.

关 键 词：拟连续DOMAIN 局部拟基 浓度 SCOTT拓扑 LAWSON拓扑 

分 类 号：O153.1[理学—数学]