Xiaoyong Xi

activity

20192022

most citedA complete Heyting algebra whose Scott space is non-sober

5 citations · 9 across the 5 of their papers we have counts for

collaborators

6 papers

math.GN2022★ 1 cited

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…

math.GN2020

$ω$ -Rudin spaces, well-filtered determined spaces and first-countable spaces

Xiaoquan Xu, Chong Shen, Xiaoyong Xi +1

We investigate some versions of $d$ -space, well-filtered space and Rudin space concerning various countability properties. The main results include: (i) if the sobrification of a $…

math.GN2019

First countability, $ω$ -well-filtered spaces and reflections

Xiaoquan Xu, Chong Shen, Xiaoyong Xi +1

We first introduce and study two new classes of subsets in $T_{0}$ spaces - $ω$ -Rudin sets and $ω$ -well-filtered determined sets lying between the class of all closures of countable…

math.GN2019

On $T_{0}$ spaces determined by well-filtered spaces

Xiaoquan Xu, Chong Shen, Xiaoyong Xi +1

We first introduce and study two new classes of subsets in $T_{0}$ spaces - Rudin sets and $\wdd$ sets lying between the class of all closures of directed subsets and that of irreduc…

math.GN2019★ 3 cited

Existence of well-filterifications of $T_{0}$ topological spaces

Guohua Wu, Xiaoyong Xi, Xiaoquan Xu +1

We prove that for every $T_{0}$ space $X$ , there is a well-filtered space $W (X)$ and a continuous mapping $η_X: X\lra W(X)$ such that for any well-filtered space $Y$ and any continuo…

math.GN2019★ 5 cited

A complete Heyting algebra whose Scott space is non-sober

Xiaoquan Xu, Xiaoyong Xi, Dongsheng Zhao

We prove that (1) for any complete lattice $L$ , the set $D (L)$ of all nonempty saturated compact subsets of the Scott space of $L$ is a complete Heyting algebra (with the…

Not every countable complete lattice is sober

ω-Rudin spaces, well-filtered determined spaces and first-countable spaces

First countability, ω-well-filtered spaces and reflections

On T0​ spaces determined by well-filtered spaces

Existence of well-filterifications of T0​ topological spaces

A complete Heyting algebra whose Scott space is non-sober

$ω$ -Rudin spaces, well-filtered determined spaces and first-countable spaces

First countability, $ω$ -well-filtered spaces and reflections

On $T_{0}$ spaces determined by well-filtered spaces

Existence of well-filterifications of $T_{0}$ topological spaces