Z-拟连续domain上的Scott拓扑和Lawson拓扑  

THE SCOTT TOPOLOGY AND LAWSON TOPOLOGY ON A Z-QUASICONTINUOUS DOMAIN

作　　者：徐晓泉[1] 刘应明[1] 

机构地区：[1]四川大学数学学院

出　　处：《数学年刊（A辑）》2003年第3期365-376,共12页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.19831040;No.19561002);教育部博士点基金;江西省主要学科跨世纪学术带头人培养基金;江西省自然科学基金

摘　　要：对一般子集系统Z,引入了Z-拟连续domain的概念,证明了Z-完备偏序集P是Z-拟连续的当且仅当P上的Z-Scott拓扑σ_z(P)在集包含序下是超连续格;Z-拟连续domain P上的Z-Scott拓扑σ_z(P)是Sober的当且仅当σ_z(P)具有Rudin性质,P赋予Z-Lawson拓扑λ_z(P)是pospace;且若P上的Z-Lawson开上集是Z-Scott开的,Z-Lawson开下集是下拓扑开的,则(P,λ_z(P))为严格完全正则序空间。For a general subset system Z, the concept of a Z-quasicontinuous domain is introduced, and the following results are proved: (1) a Z-complete poset P is Z-quasicontinuous if and only if the complete lattice of all Z-Scott open subsets of P is hypercontinuous, (2) the Z-Scott topology σZ(P) on a Z-quasicontinuous poset P is Sober if and only if σZ(P) has the Rudin property, and (3) a Z-quasicontinuous poset P endowed with the Z-Lawson topology λZ(P) is a pospace. Furthermore, if all upper Z-Lawson open subsets of P are Z-Scott open and all lower Z-Lawson open subsets of P are open in (P, w(P)), then (P, λZ(P)) is a strictly completely regular ordered space.

关 键 词：Z—拟连续domain 超连续格  Z—Scott拓扑  Z—Lawson拓扑 严格完全正则序空间 

分 类 号：O189.1[理学—数学]