7 papers · 1 filter
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…
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 of a -space , we consider the topology c…
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 -space or a metric space, must be co-sober. We give a negative answer. He and Zhao recently…
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 , the complement graph of is a \emph{KC}-space (as a subspace) and each non-singleton compact irreducible s…
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 whose Smyth power space is not co-sober, which gives a negative answer to an open problem.
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 spaces -- strong R-spaces, which are stronger than both R-spaces and strongly well-filtered spaces. It is proved that any su…
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…