抽象基上的伪e拓扑与伪ρ拓扑  

The Pseudo e-topology and the Pseudo ρ-topology on Abstract Bases

作　　者：毛徐新[1] 徐罗山[2] MAO Xu-xin;XU Luo-shan(College of Science,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China;Department of Mathematics,Yangzhou University,Yangzhou 225002,China)

机构地区：[1]南京航空航天大学理学院,江苏南京210016 [2]扬州大学数学科学学院,江苏扬州225002

出　　处：《模糊系统与数学》2019年第5期136-142,共7页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(11671008;11101212;11701500);江苏省自然科学基金资助项目(BK20170483);江苏高校品牌专业建设工程(PPZY2015B109)

摘　　要：在抽象基上引入了伪e拓扑和伪ρ拓扑,研究了这两种内蕴拓扑的性质以及与其它内蕴拓扑的关系。利用伪e拓扑与伪ρ拓扑得到具有辅助关系的偏序集的辅助基的若干等价刻画。证明了具有辅助关系的偏序集的辅助基恰是伪ρ拓扑的稠子集。The new concepts of the pseudo e-topology and the pseudo ρ-topology on abstract bases are introduced. Some basic properties of the pseudo e-topology and the pseudo ρ-topology and relations with other intrinsic topologies are explored. Via the pseudo e-topology and the pseudo ρ-topology, we obtain several characterizations of auxiliary bases of posets with auxiliary relations. It is proved that, in posets with auxiliary relations, auxiliary bases correspond exactly to dense sets with respect to the pseudo ρ-topology.

关 键 词：抽象基 辅助关系 伪e拓扑 伪ρ拓扑 辅助基 

分 类 号：O153[理学—数学] O189[理学—基础数学]