拟代数Domain的若干性质  

Some properties on quasialgebraic Domain

作　　者：赵彬[1] 梁晓荣[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）》2005年第3期1-5,共5页Journal of Shaanxi Normal University：Natural Science Edition

基　　金：国家自然科学基金资助项目(10471083);教育部"高校青年教师奖"基金资助项目(教人司[2000]26号)

摘　　要：基于拟连续Domain的等价定义及其构造,研究了拟代数Domain的一系列性质,并且给出了它的等价刻画,由此得到拟代数Domain一定是拟连续Domain.通过讨论Scott连续闭包算子保持集合与集合之间的Way below关系这一特性,证明了拟代数Domain在Scott连续闭包算子下的像仍是拟代数Domain;得到了拟代数Domain上赋予Scott拓扑构成Baire空间,拟代数格上赋予Lawson拓扑构成Priestley空间等结论.Based on the equivalent definition and construction of quasicontinuous Domain, some properties on quasialgebraic Domain are studied, and its equivalent propositions are given. Thus it can be concluded that quasialgebraic Domain is quasicontinuous Domain. By means of discussing the characteristic that Scott-continuous closure operators preserve the way below relation among sets, the fact that the image of quasialgebraic Domain under these operators is still quasialgebraic Domain is proved. It is obtained that quasialgebraic Domain with Scott topology and quasialgebraic lattice with Lawson topology are respectively Baire space and Priestley space.

关 键 词：拟连续DOMAIN 拟代数Domain 完全不连通空间 Priestley空间 

分 类 号：O153.1[理学—数学]