Xiaoquan Xu

collaborators

9 papers

math.GN2026

Compact localization and co-sobriety of Smyth power spaces

Wei Ji, Xiaoquan Xu

We establish a compact-localization theorem for finite iterates of the Smyth power space. Successive union maps assign to every finite-level Smyth object a canonical least compact…

math.GN2026

Products of co-sober spaces need not be co-sober

Xiaoquan Xu, Wei Ji

We answer negatively the question whether the product of two co-sober spaces must be co-sober. For a nonempty closed subset $A$ of a $T_{1}$ -space $(X, τ)$ , we consider the topology c…

math.GN2026

A countable metric space whose Hoare power space is not co-sober

Xiaoquan Xu, Wei Ji

Xu asked whether the Hoare power space of a co-sober space, and in particular of a $T_{2}$ -space or a metric space, must be co-sober. We give a negative answer. He and Zhao recently…

math.LO2026

Scott topologies on meet-continuous domains

Xiaoquan Xu

We study Scott products and sobriety of countable meet-continuous domains, meaning meet-continuous dcpos without any additional continuity or least-element assumption. Using the co…

math.LO2026

Every countable meet-continuous lattice is Scott sober

Xiaoquan Xu, Wei Ji

We prove that every countable meet-continuous lattice is Scott sober. For any family of such lattices, the Scott topology on the product equals the product of the factor Scott topo…

math.GN2026

School of Mathematics and Statistics, Guilin University of Technology, Guilin 541004, ChinaScott spaces of complete Boolean algebras need not be co-sober

Wei Ji, Xiaoquan Xu

In this paper, we first prove that for a complete Boolean algebra $L$ , the complement graph of $L$ is a \emph{KC}-space (as a subspace) and each non-singleton compact irreducible s…

math.GN2026

Smyth power space of a co-sober space is not always co-sober

Xiaoquan Xu, Fengshuo Xu, Haitao Ji +1

In this paper, we give a co-sober space $X$ whose Smyth power space $P_{S} (X)$ is not co-sober, which gives a negative answer to an open problem.

math.GN2025

Strong well-filteredness of upper topology on sup-complete posets

Xiaoquan Xu, Yi Yang, Lizi Chen

We first introduce and investigate a new class of $T_{0}$ spaces -- strong R-spaces, which are stronger than both R-spaces and strongly well-filtered spaces. It is proved that any su…

math.GN2025

Countable quasicontinuous domains are quasialgebraic

Xiaoquan Xu

We prove that every quasicontinuous domain that fails to be quasialgebraic admits the unit interval [0, 1] as its monotone Lawson-continuous image. As a result, every countable qua…