δ-sober空间及其性质  

δ-sober Spaces and Its Properties

作　　者：王武[1] 谭彬[2] 张舜 WANG Wu;TAN Bin;ZHANG Shun(Basic Course Department of Zhonghuan Information College,Tianjin University of Technology,Tianjin 300380,China;School of Science,Tianjin University of Technology,Tianjin 300384,China;Mathematics Teaching Department of Tianjin Ren’ai College,Tianjin 301636,China)

机构地区：[1]天津理工大学中环信息学院基础课部,天津300380 [2]天津理工大学理学院,天津300384 [3]天津仁爱学院数理教学部,天津300163

出　　处：《计算机科学》2023年第S02期536-539,共4页Computer Science

基　　金：天津市教委科研计划项目(2018KJ147);2021年高等学校大学数学教学研究与发展中心教学改革项目(CMC20210115)。

摘　　要：文中讨论了δ-sober空间的一些基本性质,引入了s_(2)-弱收敛空间的概念,并讨论了δ-sober空间和s_(2)-弱收敛空间的关系。主要结论有:(1)δ-sober空间的子空间为δ-sober空间;(2)设(X,τ)为IDC空间,则(X,τ)为s_(2)-弱收敛空间当且仅当(X,τ)为δ-sober空间;(3)s_(2)-弱收敛的IDC空间上的拓扑τ与在特殊化序下的σ_(2)-拓扑一致,并且O(X)=O_(σ2)(X)=O_(SI_(2))(X);(4)设(X,τ)为SI_(2)-拟连续空间,则(X,τ_(SI_(2)))为δ-sober空间;(5)设(X,τ)为δ-sober的局部超紧空间,则(X,τ)为s_(2)-拟连续偏序集。This paper discusses some basic properties ofδ-sober spaces,introduces the concept of s_(2)-weakly convergent spaces,and discusses the relationship betweenδ-sober spaces and s_(2)-weakly convergent spaces.The main conclusions are as follows:1)The subspaces ofδ-sober spaces areδ-sober spaces.2)If(X,τ)is an IDC space,then it is an s_(2)-weakly convergence space if and only if it is aδ-sober space.3)The topology on the s_(2)-weakly convergence IDC space is consistent with the σ_(2)-topology and O(X)=Oσ2(X)=O SI 2(X).4)If(X,τ)is an SI 2-quasicontinuous space,then it is aδ-sober space.5)Let(X,τ)be a locally hypercompactδ-sober space,then it is an s_(2)-quasi continuous poset.

关 键 词：SI_(2)-连续 SI_(2)-拓扑 δ-sober空间 s_(2)-弱收敛 IDC空间 

分 类 号：O153.1[理学—数学] O189.1[理学—基础数学]