6 papers
Uniqueness of Bound States for Double-Power Scalar Field Equations
Yujin Guo, Wei Ji, Yong Luo
We study the uniqueness of bound states for the following scalar field equation $$ -Δu+u=-\varepsilon |u|^{q-1}u+|u|^{p-1}u \,\ \ \mbox{in}\,\ \mathbb R^N, \,\ \varepsilon>0,\tag*{…
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…
Scott products and sobriety of countable meet-continuous dcpos
Xiaoquan Xu, Wei Ji
We study Scott-product compatibility and sobriety for countable meet-continuous directed-complete partial orders (dcpos). We construct a countable meet-continuous dcpo …
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…