5 citations · 22 across the 32 of their papers we have counts for
7 papers · 1 filter
First countability, -well-filtered spaces and reflections
Xiaoquan Xu, Chong Shen, Xiaoyong Xi +1
We first introduce and study two new classes of subsets in spaces - -Rudin sets and -well-filtered determined sets lying between the class of all closures of countable…
A direct approach to -reflections of spaces
Xiaoquan Xu
In this paper, we provide a direct approach to -reflections of spaces. For a full subcategory of the category of all spaces and a space $…
On topological Rudin's lemma, well-filtered spaces and sober spaces
Xiaoquan Xu, Dongsheng Zhao
Based on topological Rudin's Lemma, we investigate two new kinds of sets - Rudin sets and well-filtered determined sets in topological spaces. Using such sets, we formulate a…
On spaces determined by well-filtered spaces
Xiaoquan Xu, Chong Shen, Xiaoyong Xi +1
We first introduce and study two new classes of subsets in spaces - Rudin sets and $\wdd$ sets lying between the class of all closures of directed subsets and that of irreduc…
On some kinds of weakly sober spaces
Xinpeng Wen, Xiaoquan Xu
In \cite{E_2018}, Erné relaxed the concept of sobriety in order to extend the theory of sober spaces and locally hypercompact spaces to situations where directed joins were missing…
Existence of well-filterifications of topological spaces
Guohua Wu, Xiaoyong Xi, Xiaoquan Xu +1
We prove that for every space , there is a well-filtered space and a continuous mapping $η_X: X\lra W(X)$ such that for any well-filtered space and any continuo…
A complete Heyting algebra whose Scott space is non-sober
Xiaoquan Xu, Xiaoyong Xi, Dongsheng Zhao
We prove that (1) for any complete lattice , the set of all nonempty saturated compact subsets of the Scott space of is a complete Heyting algebra (with the…