序收敛的Dedekind-Macneille完备遗传保持性  

The Dedekind-Macneille Completion Hereditary for Order-convergence in Posets

作　　者：孙涛[1] 李庆国[2] SUN Tao;LI Qing-guo(College of Mathematics and Physics,Hunan University of Arts and Science,Changde 415000,China;School of Mathematics,Hunan University,Changsha 410082,China)

机构地区：[1]湖南文理学院数理学院,湖南常德415000 [2]湖南大学数学学院,湖南长沙410082

出　　处：《模糊系统与数学》2024年第3期8-15,共8页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(11901194);湖南省教育厅科学基金资助项目(21B0617)。

摘　　要：本文考虑序收敛的Dedekind-Macneille完备遗传保持问题。引入e^(*)-弱双连续偏序集的概念,给出了偏序集上序收敛是Dedekind-Macneille完备遗传保持的必要条件是该偏序集具有有界与e^(*)-弱双连续性,特别地,证明了具有性质B的偏序集上序收敛是Dedekind-Macneille完备遗传保持的当且仅当该偏序集是有界目e^(*)-弱双连续的。序收敛的Dedekind-Macneille完备遗传保持性问题是格序理论发展早期所遗留的基本问题,本文所给出的结果进一步地解决了该问题,这对格序理论基础的完善与发展具有重要意义。We study in this paper the Dedekind-MacNeille completion hereditary for order-convergence in posets.By introducing the notion of e^(*)-weakly double continuous posets,a necessary condition for the order-convergence being Dedekind-MacNeille completion hereditary is obtained that is,if the order-convergence in a poset is Dedekind-Mac-Neille completion hereditary,then the poset is bounded and e^(*)-weakly double continuous.In particular,it is proved that in a poset with Property B,the order-convergence is Dedekind-MacNeille completion hereditary if and only if the poset is bounded and e^(*)-weakly double continuous.The problem that characterizes the posets for order-convergence being Dedekind-MacNeille completion hereditary is fundamental in the early days of the study of Lattice and Order Theory.In this paper,we give some further results on the problem.and it will be significative for the development of Lattice and Order Theory.

关 键 词：序收敛 Dedekind-Macneille完备遗传保持 e^(*)-弱双连续偏序集 

分 类 号：O153.1[理学—数学]