5 citations · 7 across the 13 of their papers we have counts for
7 papers · 1 filter
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…