5 citations · 16 across the 22 of their papers we have counts for
23 papers
Scott--Isbell Coincidence for Continuous Dcpos beyond Bicompleteness
Yuxu Chen, Yunjie Wen, Xiaoyong Xi
Lawson and Mislove posed the following problem in 1990 as Problem~535 in \emph{Open Problems in Topology}: for a core-compact space \(X\) and a dcpo \(P\) equipped with its Scott t…
Sobriety of Regular Open Algebras in Second-Countable T3 Spaces
Xiaoyong Xi, Chong Shen, Dongsheng Zhao
For a topological space X, let RO(X) be the complete Boolean algebra of regular open subsets of X, ordered by inclusion. We prove that, for every second-countable T3 space X, the S…
A Quasicontinuous Domain Without an Interval Retract
Chong Shen, Xiaoyong Xi, Dongsheng Zhao
We give negative answers to two questions of X.Xu concerning the occurrence of the unit interval in nonquasialgebraic quasicontinuous domains. We construct, directly from the binar…
The set of real numbers with the cocountable topology has a bounded complete dcpo model
Dongsheng Zhao, Chong Shen, Xiaoyong Xi
We construct a bounded complete dcpo P whose maximal point space is homeomorphic to the set R of all reals equipped with the cocountable topology, thereby answering an open problem…
The complete Boolean algebra of regular open sets in real line is not sober
Xiaoyong Xi, Chong Shen, Dongsheng Zhao
Whether the Scott space of the complete Boolean algebra $\RO(\bbR)$ of regular open subsets in the real line is sober was explicitly recorded as an open problem by Xu and Zhao and…
Scott Function Spaces under One-Sided FS Assumptions: Counterexamples, Positive Results, and New Directions
Chong Shen, Weng Kin Ho, Xiaoyong Xi +1
The class of FS-domains is known to be closed under Scott function spaces when both the source and target are FS-domains. This paper investigates what remains true under one-sided…
Convergence Choquet-complete spaces and domain representations
Xiaoyong Xi, Chong Shen, Weng Kin Ho +1
de Brecht, Goubault-Larrecq, Jia and Lyu asked whether every sober convergence Choquet-complete space is domain-complete. We introduce the notion of singleton Choquet-completeness,…
The answers to two problems on dcpo models
Chong Shen, Xiaoyong Xi, Dongsheng Zhao
A poset model of a topological space is a poset such that is homeomorphic to the maximal point space of (the set Max() of all maximal points of equipped with…
Notes on countable frames
Xiaodong Jia, Xiaoyong Xi
Matthew de Brecht raised the question of whether countable frames are continuous lattices. We prove that the continuity of a countable frame implies the quasicontinuity of its corr…
The answers to two problems on maximal point spaces of domains
Xiaoyong Xi, Chong Shen, Dongsheng Zhao
A topological space is domain-representable (or, has a domain model) if it is homeomorphic to the maximal point space $\mbox{Max}(P)$ of a domain (with the relative Scott topol…
Products of two sober dcpo's need not be sober
Hualin Miao, Xiaoyong Xi, Xiaodong Jia +2
We construct two dcpo's whose Scott spaces are sober, but the Scott space of their order product is not sober. This answers an open problem on the sobriety of Scott spaces. Meantim…
The set of maximal points of an -domain need not be a -set
Gaolin Li, Chong Shen, Kaiyun Wang +2
A topological space has a domain model if it is homeomorphic to the maximal point space $\mbox{Max}(P)$ of a domain . Lawson proved that every Polish space has an -domain…
Further studies on open well-filtered spaces
Chong Shen, Xiaoyong Xi, Dongsheng Zhao
The open well-filtered spaces were introduced by Shen, Xi, Xu and Zhao to answer the problem whether every core-compact well-filtered space is sober. In the current paper we explor…
On Scott power spaces
Xiaoquan Xu, Xinpeng Wen, Xiaoyong Xi
In this paper, we mainly discuss some basic properties of Scott power spaces. For a space , let be the poset of all nonempty compact saturated subsets of $…
Not every countable complete lattice is sober
Hualin Miao, Xiaoyong Xi, Qingguo Li +1
The study of the sobriety of Scott spaces has got an relative long history in domain theory. Lawson and Hoffmann independently proved that the Scott space of every continuous direc…
The reflectivity of some categories of T0 spaces in domain theory
Chong Shen, Xiaoyong Xi, Dongsheng Zhao
Keimel and Lawson proposed a set of conditions for proving a category of topological spaces to be reflective in the category of all T0 spaces. These conditions were recently used t…
-Rudin spaces, well-filtered determined spaces and first-countable spaces
Xiaoquan Xu, Chong Shen, Xiaoyong Xi +1
We investigate some versions of -space, well-filtered space and Rudin space concerning various countability properties. The main results include: (i) if the sobrification of a $…
On open well-filtered spaces
Chong Shen, Xiaoyong Xi, Xiaoquan Xu +1
We introduce and study a new class of spaces, called open well-filtered spaces. The main results we proved include (1) every well-filtered space is an open well-filtered spac…
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…
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…
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…
The Ho-Zhao Problem
Weng Kin Ho, Jean Goubault-Larrecq, Achim Jung +1
Given a poset , the set, , of all Scott closed sets ordered by inclusion forms a complete lattice. A subcategory of (the category of posets a…