S*-收敛和局部强紧空间
S*-convergence and locally hypercompact spaces
陈俣旭 1寇辉1
作者信息
摘要
定向空间是定向完备偏序集的拓扑推广,局部强紧空间可以刻画为拟连续的定向空间.本文给出了关于局部强紧空间的一个拓扑版的 Scott 收敛定理.通过引入 S*-收敛的概念并定义有限逼近空间,本文得到以下主要结果:(i)定向空间 X 是局部强紧的当且仅当 S*X-收敛是可拓扑化的;(ii)对任意 T0 空间X,S*X-收敛是可拓扑化的当且仅当 X 是有限逼近空间;(iii)若定向空间 X 上的 Lawson 拓扑是紧的,则 X 是赋予 Scott 拓扑的定向完备偏序集.
Abstract
Locally hypercompact spaces can be characterized as quasicontinuous monotone determined spaces,where monotone determined spaces are topological extensions of dcpos in domain theory.In this pa-per,we give a topological version of the Scott convergence theorem for locally hypercompact spaces.By intro-ducing the notion of S*-convergence and defining the notion of finitely approximated spaces,the following main results are obtained:(i)A monotone determined space X is locally hypercompact iff S*X-convergence is topological;(ii)For a T0 space X,S*X-convergence is topological iff X is a finitely approximating space;(iii)If the Lawson topology on a monotone determined space X is compact,then X is a dcpo endowed with the Scott topology.
关键词
S*-收敛/定向空间/局部强紧空间/Lawson拓扑Key words
S*-convergence/Monotone determined space/Locally hypercompact space/Lawson topology引用本文复制引用
基金项目
国家自然科学基金(12231007)
国家自然科学基金(11871353)
国家自然科学基金(12001385)
出版年
2024
国家科技期刊平台
NSTL
万方数据