半连续格上的半基,se-拓扑和sρ-拓扑  

Semi-bases,se-Topology,sρ-Topology of semicontinuous lattices

作　　者：毛徐新 徐罗山[2] MAO Xu-xin;XU Luo-shan(College of Mathematics,Nanjing Univ.of Aeronautics and Astronautics,Nanjing 210016,China;School of Math.Sci.,Yangzhou Univ.,Yangzhou 225002,China)

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

出　　处：《高校应用数学学报(A辑)》2023年第4期471-477,共7页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(11671008,11101212,11701500);江苏省高校自然科学基金(15KJD110006)。

摘　　要：在完备格上引入了se-拓扑和sρ-拓扑的概念,讨论了半连续格上se-拓扑和sρ-拓扑的一些基本性质,进而给出了半连续格上半基的若干等价刻画.In this paper,the concepts ofthe se-topology and the sρ-topologyon completelattices are introduced.Some basic properties of the se-topology and the sρ-topology on semicontinuous lattices are investigated.In terms of the se-topology and the sρ-topology,some characterizations of semi-bases of semicontinuous lattices are obtained.It is proved that semi-bases coincide with dense sets in the sρ-topology of complete lattices under certain conditions.

关 键 词：半连续格 半基 se-拓扑 sρ-拓扑 

分 类 号：O153.1[理学—数学] O189.1[理学—基础数学]