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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 of a -space , 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 -space or a metric space, must be co-sober. We give a negative answer. He and Zhao recently…