半连续dcpo  

Semicontinuous dcpos

作　　者：刘玉连[1] 李高林[1,2] 徐罗山[1] 

机构地区：[1]扬州大学数学科学学院,江苏扬州225002 [2]盐城师范学院数学科学学院,江苏盐城224002

出　　处：《扬州大学学报（自然科学版）》2012年第2期1-5,共5页Journal of Yangzhou University：Natural Science Edition

基　　金：国家自然科学基金资助项目(61074129;61103018;11101352);江苏省自然科学基金资助项目(BK2010313;BK2011442);国家重点实验室开放课题(SKLSDE-2011KF-08);盐城师范学院资助项目(11YCKL001)

摘　　要：作为半连续格的推广,引入半素集和半连续dcpo的概念,并讨论半连续dcpo的性质,在半连续dcpo中得到类似于半连续格的一些主要结果.同时研究了dcpo的内蕴拓扑——半Scott拓扑、半Lawson拓扑,证明了上集U半Lawson开当且仅当U为半Scott开,下集U半Lawson闭当且仅当U为半Scott闭.最后研究了半连续映射,证明了若保序映射f半连续,则f关于半Scott拓扑是连续映射.As a generalization of semicontinuous lattices, the concepts of serniprime sets and semi- continuous dcpos are introduced. Basic properties of semicontinuous dcpos are discussed. The main results of the theory of semicontinuous lattices are carried to semicontinuous dcpo. Moreover, some intrinsic topologies--the semi-Scott topology and the semi-Lawson topology on semicontinuous dcpos are investigated. It is proved that an upper set U is semi-Lawson open iff it is semi-Scott open; a lower set U is semi-Lawson closed iff it is semi-Scott closed. Finally the concept of semicon- tinuous mapping is introduced, it is showed that if f is order preserving and semicontinuous, then f is continuous with respect to the semi-Scott topologies.

关 键 词：半素集 半连续dcpo 半Scott拓扑 半连续映射 

分 类 号：O153.1[理学—数学] O189.1[理学—基础数学]