摘要
本文主要讨论超sober空间的一些基本性质,对三类特殊空间的超sober性进行了讨论,并对T_(0)空间X的超sober性与其Smyth幂空间、Hoare幂空间的超sober性之间的关系进行了讨论;用反例说明了可数无限多个超sober空间的乘积一般不是超sober的;证明了若T_(0)空间X不是超sober的,则其超sober化不存在。
This paper mainly discusses some basic properties of hyper-sober space.The hyper-soberity of three kinds of special spaces are investigated.Some relations between the hyper-soberity of a T_(0)space Xand that of its Smyth power space and Hoare power space are investigated.A counter example is given to show that the product of acountable infinite family of hyper-sober spaces is not hyper-sober in general.It is proved that if a T_(0)space Xis not hyper-sober,then its hyper-sobrification does not exist.
作者
温娜娜
徐晓泉
WEN Na-na;XU Xiao-quan(College of Math.and Statistics,Jiangxi Normal University,Nanchang 330022,China)
出处
《模糊系统与数学》
北大核心
2023年第4期165-174,共10页
Fuzzy Systems and Mathematics
基金
国家自然科学基金资助项目(12071199
11661057)
“赣鄱英才555工程”科技领军人才培养计划项目
江西省自然科学基金重点项目(20192ACBL20045)
