5 citations · 22 across the 19 of their papers we have counts for
19 papers
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,…
Sober topologies on a set
Xiangrui Li, Qingguo Li, Dongsheng Zhao
The collection of all topologies on a set X forms a complete lattice with respect to the inclusion order, which have been investigated by many researchers. Sobriety is one of the c…
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…
The sheaf representation of residuated lattices
Huarong Zhang, Dongsheng Zhao
The residuated lattices form one of the most important algebras of fuzzy logics and have been heavily studied by people from various different points of view. Sheaf presentations p…
Quasiexact posets and the moderate meet-continuity
Zhaorong He, Zhongqiang Yang, Dongsheng Zhao
The study of weak domains and quasicontinuous domains leads to the consideration of two types generalizations of domains. In the current paper, we define the weak way-below relatio…
One-step closure, weak one-step closure and meet continuity
Hualin Miao, Qingguo Li, Dongsheng Zhao
This paper studies the weak one-step closure and one-step closure properties concerning the structure of Scott closures. We deduce that every quasicontinuous domain has weak one-st…
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 $…
Some open problems on well-filtered spaces and sober spaces
Xiaoquan Xu, Dongsheng Zhao
In the past few years, the research on sober spaces and well-filtered spaces has got some breakthrough progress. In this paper, we shall present a brief summarising survey on some…
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…
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…
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…
Uniqueness of directed complete posets based on Scott closed set lattices
Dongsheng Zhao, Luoshan Xu
In analogy to a result due to Drake and Thron about topological spaces, this paper studies the dcpos (directed complete posets) which are fully determined, among all dcpos, by thei…
Faithfulness of Directed Complete Posets based on Scott Closed Set Lattices
Dongsheng Zhao, Luoshan Xu
By Thron, a topological space has the property that isomorphic to implies is homeomorphic to iff is sober and , where and denote th…
Join-continuity + Hypercontinuity = Prime continuity
Weng Kin Ho, Achim Jung, Dongsheng Zhao
A remarkable result due to Kou, Liu & Luo states that the condition of continuity for a dcpo can be split into quasi-continuity and meet-continuity. Their argument contained a gap,…