Xiaoquan Xu

collaborators

4 papers

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…