偏序集上的弱Scott拓扑与弱测度拓扑  

Weak Scott Topology and Weak Measure Topology on Posets

作　　者：王武[1] 李旭东[1] WANG Wu;LI Xudong(Zhonghuan Information College,Tianjin University of Technology,Tianjin 300380)

机构地区：[1]天津理工大学中环信息学院,天津300380

出　　处：《四川师范大学学报（自然科学版）》2024年第2期264-268,共5页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(11871353);天津市教委科研计划项目(2018KJ147)

摘　　要：讨论偏序集的s_(2)连续性和弱Scott拓扑的一些性质:给出s_(2)连续偏序集上伴随的一些性质;定义弱测度拓扑,研究s_(2)连续偏序集上弱测度拓扑的性质;利用弱测度拓扑给出s_(2)交连续偏序集的等价刻画;研究弱Scott拓扑的连通性.Some properties of s_(2)continuous posets and weak Scott topology of posets are discussed.The main contents are as follows:some properties of adjoint on s_(2)continuous posets are given;weak measure topology is defined,and the properties of weak measure topology on s_(2)continuous posets are studied;by using weak measure topology,the equivalent characterization of s_(2)meet continuous poset is given;the connectivity of weak Scott topology is studied.

关 键 词：偏序集 s_(2)连续 伴随 弱Scott拓扑 弱测度拓扑 连通性 

分 类 号：O153.1[理学—数学] O189.1[理学—基础数学]