5 citations · 11 across the 11 of their papers we have counts for
11 papers · 1 filter
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…
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…
-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…