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Tag Archives: core-compactness
When do products distribute over colimits in Top?
In a recent paper, Lawson and Xu give a new class of posets on which the Scott topology of the (poset) product of two posets coincides with the product topology (of each poset with its Scott topology). I will explain … Continue reading
Posted in Uncategorized
Tagged colimit, core-compactness, counterexample, filters, product
Comments Off on When do products distribute over colimits in Top?
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)
When do the upper (a.k.a., lower Vietoris) and Scott topologies coincide on the Hoare hyperspace of a space?
I would like to talk about a nifty, recent result due to Yu Chen, Hui Kou, and Zhenchao Lyu. There are two natural topologies on the Hoare hyperspace of a space X, the Scott and the lower Vietoris topology, and … Continue reading
Posted in Uncategorized
Tagged core-compactness, first-countability, hyperspace, powerdomain, Scott topology, Vietoris topology
Comments Off on When do the upper (a.k.a., lower Vietoris) and Scott topologies coincide on the Hoare hyperspace of a space?
Irredundant families, the Smyth powerdomain, the Lyu-Jia theorem, and the baby Groemer theorem
A ∩-semilattice of sets is a family of sets that is closed under finite intersections, and it is irredundant if and only if all its non-empty elements are irreducible. That sounds like a ridiculously overconstrained notion, but I will give … Continue reading
Posted in Uncategorized
Tagged compactness, core-compactness, hyperspace, powerdomain
Comments Off on Irredundant families, the Smyth powerdomain, the Lyu-Jia theorem, and the baby Groemer theorem
Core-compact+well-filtered T0=sober locally compact
Last time, I motivated the construction of the well-filterification Wf(X) of a space X of X. Xu, Ch. Shen, X. Xi and D. Zhao by saying that it was needed to understand their proof of the fact that every core-compact … Continue reading
Posted in Uncategorized
Tagged core-compactness, sober space, well-filtered space
Comments Off on Core-compact+well-filtered T0=sober locally compact