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Meta
Author Archives: jgl
Revisiting Stone duality for bitopological spaces: II. sequent theories, 2-sublocales, and (simple) biframes
What a summer! Yuxu Chen, Hui Kou and Zhenchao Lyu cracked three open problems in domain theory, and I have talked about one in the July 2026 post. But let us change subjects for a while, and let us go … Continue reading
Posted in Uncategorized
Tagged 2-frame, biframe, bitopological space, frame, sequent theory, sieve, sublocale
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FS≠RB
Great news this month! Yuxu Chen, Hui Kou and Zhenchao Lyu, from the University of Sichuan in Chengdu, have finally cracked the problem whether FS-domains and RB-domains are the same notion, and they are not. This problem had been open … Continue reading
Posted in Uncategorized
Tagged FS-domain, Lorentz cone, matrix cone, RB-domain
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Revisiting Stone duality for bitopological spaces
Exactly one year ago, I presented a form of Stone duality for bitopological spaces due to Jung and Moshier, and refined by Jakl. This relied on a notion called d-frames, which are a pair of frames linked by a totality … Continue reading
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Tagged 2-frame, bitopological space, d-frame, Stone duality
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≪-separating domains and FS-domains
Achim Jung’s category of FS-domains is one of the two maximal cartesian-closed categories of continuous dcpos. Very recently, Wei Luan proposed a variation on the notion, and which he calls ≪-separating domains. One of his main theorems is that given … Continue reading
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Tagged cartesian closeness, continuous dcpo, FS-domain, RB-domain
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Choquet-Wilker spaces
A Choquet-Wilker space is a space in which the collection of compact saturated subsets is rich: one where, given a compact saturated set Q included in a union U1 ∪ U2 of two open sets, Q is included in a … Continue reading
Posted in Uncategorized
Tagged Alexandroff compactification, Choquet-Wilker space, consonance, KC-space, KT4 space, LCS-complete, locally compact
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Appert space
Some time ago, I was wondering about the various definitions of a Radon measure, and in particular about the relation between local finiteness and the requirement that the measure of every compact subset be finite. (I will explain everything.) The … Continue reading
Posted in Uncategorized
Tagged counterexample, first-countability, zero-dimensional spaces
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Characterizing non-ω-well-filtered spaces by forbidden subspaces
In a 2023 paper, Hualin Miao, Xiaodong Jia, Chong Shen and Qingguo Li characterized ω-well-filtered spaces as those that do not contain any one of two very simple spaces, S1 and SD, as Skula-closed subspaces. This is part of a … Continue reading
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Tagged forbidden substructures, sobriety, well-filtered space
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Stone duality for preordered topological spaces II. Ad-frames
A preordered topological space is a topological space X with a preordering ≤. I wish to explain a form of Stone duality for such preordered topological spaces. The idea is pretty simple: last time, we have seen a form of Stone duality for … Continue reading
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Stone duality for preordered topological spaces I. Bonsangue-Jacobs-Kok duality for preorders
We know a lot of Stone-like dualities, and I would like to start exploring a form of Stone duality for preordered topological spaces. We start with a simple problem this month: duality for preordered sets; hence, no topology (yet) in … Continue reading
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Knijnenburg’s dcpo, weakly Hausdorff spaces and lenses
In 1993, Knijnenburg studied lenses, and came up with a simple dcpo that shows that the topological and the ordinary Egli-Milner orderings on lenses can differ. This dcpo settles more than this question. For example, it is an algebraic dcpo … Continue reading
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