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Meta
Tag Archives: countability
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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On products of dcpos, the Miao-Xi-Li-Zhao lemma, and the complete lattice Lfan (part I)
The product of a poset P with itself can be given two topologies: the Scott topology of the product, or the product of the Scott topologies. Those two topologies differ in general, but they coincide when P is a continuous … Continue reading
Posted in Uncategorized
Tagged core-compactness, countability, first-countability, Hoare hyperspace, ideals, Scott topology
Comments Off on On products of dcpos, the Miao-Xi-Li-Zhao lemma, and the complete lattice Lfan (part I)