Xiaodong Jia

collaborators

4 papers

math.GN2025

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…

math.GN2025

Separating domains from algebraic domains

Xiaodong Jia, Qingguo Li, Wei Luan

We prove that every domain that fails to be algebraic admits the unit interval $[0, 1]$ as its Scott-continuous retract. As a result, every countable domain is algebraic.

math.GN2024

$I ¨ $ -well-filtered spaces, revisited

Hualin Miao, Xiaodong Jia, Ao Shen +1

We prove that a $T_{0}$ topological space is $I ¨ $ -well-filtered if and only if it does not admit either the natural numbers with the cofinite topology or with the Scott topology as i…

cs.LO2024

The category of well-filtered dcpos is not $I^$ -faithful

Hualin Miao, Huijun Hou, Xiaodong Jia +1

The Ho-Zhao problem asks whether any two dcpo's with isomorphic Scott closed set lattices are themselves isomorphic, that is, whether the category $DCPO$ of dcpo's and Sco…

Products of two sober dcpo's need not be sober

Separating domains from algebraic domains

I¨-well-filtered spaces, revisited

The category of well-filtered dcpos is not I^-faithful

$I ¨ $ -well-filtered spaces, revisited

The category of well-filtered dcpos is not $I^$ -faithful