A direct characterization of the monotone convergence space completion
A direct characterization of the monotone convergence space completion
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DOI：
10.1016/j.topol.2017.08.008
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发表时间：
2017-10
影响因子：
0.6
通讯作者：
Zhongxi Zhang;Qingguo Li
中科院分区：
文献类型：
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作者：
Zhongxi Zhang;Qingguo Li
对于 T 0-空间 X 和 X 的所有闭子集的集合 Г (X)，具有下 Vietoris 拓扑的 Г (X) 中 X 的所有点闭包的 d-闭包称为 X 的标准 D-完成。本文通过引入锥形集的概念，给出了 D-完成的直接表征：具有下 Vietoris 拓扑的 X 的所有锥形闭子集的集合正是标准 D-X 的完成。
For a T 0-space X and the set Γ (X) of all closed subsets of X, the d-closure of all point closures of X in Γ (X) endowed with the lower Vietoris topology is called the standard D-completion of X. In this paper, by introducing the notion of a tapered set, we present a direct characterization of the D-completion: the set of all tapered closed subsets of X endowed with the lower Vietoris topology is exactly the standard D-completion of X.