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Tag Archives: weak Hausdorffness
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
Posted in Uncategorized
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
Posted in Uncategorized
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
Comments Off on Weakly Hausdorff spaces, and locally strongly sober spaces