相对连续偏序集及其应用  

Relative continuous posets and its application

作　　者：刘东明 姜广浩[1] 李辉 LIU Dongming;JIANG Guanghao;LI Hui(School of Mathematical Science,Huaibei Normal University,Huaibei 235000,Anhui Province,China)

机构地区：[1]淮北师范大学数学科学学院,安徽淮北235000

出　　处：《天津师范大学学报（自然科学版）》2018年第4期13-16,共4页Journal of Tianjin Normal University：Natural Science Edition

基　　金：国家自然科学基金资助项目(11361028);安徽高等学校省级自然科学研究重点资助项目(KJ2017A378);淮北师范大学研究生创新基金资助项目(2017yjscx07);淮北师范大学研究生教育教学研究资助项目(2017jyxm03)

摘　　要：提出相对定向集和相对定向完备集的概念,并在相对定向完备集上引入相对双小于关系.利用相对way below关系引入相对连续偏序集的概念,探讨了其一些等价条件,并证明了相对连续偏序集具有相对T的遗传性.The concepts of relative directed set and relative directed complete set are presented,and the relative way below relation is introduced and some its properties are studied. On this basis,the concept of relative continuous poset is intro-duced and its equivalence conditions are discussed. And then the conclusion that relative continuous poset has the property of relative heredity of set T is obtained.

关 键 词：相对定向完备集 相对way below关系 相对连续偏序集 相对遗传性 

分 类 号：O153.1[理学—数学]