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Tag Archives: sobriety
Bitopological spaces, d-frames, and Jung-Moshier duality
Stone duality is an adjunction between the category Top of topological spaces and the category Loc of locales, namely the opposite of the category Frm of frames. Is there a similar-looking adjunction between the category biTop of bitopological spaces—namely, sets … Continue reading
Posted in Uncategorized
Tagged bitopological space, monad, sober space, sobriety, Stone duality
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The complete lattice Lfan (part II)
Last time, we had started to study the complete lattice Lfan, namely just N × N, with equality as ordering on the first component and the usual ordering on the second component, plus an extra bottom element ⊥, plus an … Continue reading
Posted in Uncategorized
Tagged conformity, consonance, maximal limit space, Scott topology, Smyth hyperspace, sobriety, weak Hausdorffness
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Hoover’s maximal limit spaces II: products, liftings, retracts, function spaces, and hyperspaces
Last time, we had introduced Hoover’s maximal limit spaces: spaces in which every convergent filter has a unique largest limit. That notion is closed under many constructions, as we will see: products, liftings, retracts, notably, and that is elementary. The … Continue reading
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Tagged coherence, convergence, filters, function space, hyperspace, sobriety, strong sobriety, weak Hausdorffness
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Hoover’s maximal limit spaces I: local strong sobriety, bounded sup-completeness and weak Hausdorffness
In 1995, Douglas Hoover introduced and studied a notion of maximal limit spaces: spaces in which every convergent net has a unique largest limit. This has connections with many other kinds of spaces that we have explored already, and I … Continue reading
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Tagged coherence, convergence, filters, sobriety, strong sobriety, weak Hausdorffness
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Weakly Hausdorff spaces, and locally strongly sober spaces
A funny convergence of topics happened a few weeks ago. Frédéric Mynard told me about so-called locally strongly sober spaces (which, I am ashamed to say, I had heard about but completely forgotten about). At the same time, I was … Continue reading
Posted in Uncategorized
Tagged coherence, convergence, filters, sobriety, strong sobriety, weak Hausdorffness
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