拟连续Domain的SM^(*)性质  

SM^(*) Property of Quasi-Continuous Domain

作　　者：王武[1] 谭彬[2] 张舜 WANG Wu;TAN Bin;ZHANG Shun(Department of Basic Course,Zhonghuan Information College,Tianjin University of Technology,Tianjin 300380,China;College of Science,Tianjin University of Technology,Tianjin 300384,China;Department of Mathematics Teaching,Tianjin Ren ai College,Tianjin 300163,China)

机构地区：[1]天津理工大学中环信息学院基础课部,天津300380 [2]天津理工大学理学院,天津300384 [3]天津仁爱学院数理教学部,天津300163

出　　处：《西南师范大学学报（自然科学版）》2023年第6期25-30,共6页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家青年自然科学基金项目(11401435);天津市教委科研计划项目(2018KJ147);2021年高等学校大学数学教学研究与发展中心教学改革项目(CMC20210115)。

摘　　要：研究了拟连续Domain中比M^(*)性质更强的SM^(*)性质,并得到了一些有意义的结论.主要结果有:给出了拟连续Domain具有M^(*)性质的等价刻画;给出了拟连续Domain的SM^(*)性质的定义,并说明了M^(*)性质与SM^(*)性质的关系;给出了QL-Domain具有SM^(*)性质的等价条件;给出了两类具有性质SM^(*)的特殊的拟连续Domain.In this paper,the SM^(*) property which is stronger than the M^(*) property is studied in quasi-continuous Domain and some meaningful conclusions are obtained.The main results are as follows:the equivalent characterization of quasi-continuous Domain with the property of M^(*) is given;The definition of property of quasi-continuous Domain is given,and the relationship between the SM^(*) property and the M^(*) property is illustrated.Meanwhile,the equivalent conditions that QL-Domain has the SM^(*) property are given;Two kinds of special quasi-continuous Domains with property SM^(*) are given.

关 键 词：拟连续DOMAIN M*性质 SM^(*)性质 qmub-完备 

分 类 号：O153.1[理学—数学] O189.1[理学—基础数学]