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Tag Archives: Smyth hyperspace
Proper maps, quasi-adjoints and the Smyth hyperspace
This month, I would like to talk about proper maps, a nifty equivalent characterization through something I call quasi-adjoints and which involves the Smyth hyperspace monad, with a few non-trivial applications. Read the full post.
Posted in Uncategorized
Tagged continuous valuation, Hoare hyperspace, proper map, quasi-adjoint, Smyth hyperspace
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When is ℒ(X) locally compact?
Let ℒ(X) be the dcpo of all lower semicontinuous maps from a space X to R+ ∪ {∞}. We give it the Scott topology. Under which conditions on X is it locally compact? We will see that this happens exactly … Continue reading
Posted in Uncategorized
Tagged consonance, countability, Hoare hyperspace, Scott topology, Smyth hyperspace
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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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