Tag Archives: first-countability

On products of dcpos, the Miao-Xi-Li-Zhao lemma, and the complete lattice Lfan (part I)

Posted on May 20, 2024 by jgl

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 →

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When do the upper (a.k.a., lower Vietoris) and Scott topologies coincide on the Hoare hyperspace of a space?

Posted on March 20, 2022 by jgl

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 →

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First-countable spaces and their Smyth powerdomain

Posted on June 22, 2021 by jgl

This month, we will look at certain conditions recently found by He, Li, Xi and Zhao in 2019, and then by Xu and Yang in 2021, in order to ensure that the Smyth powerdomain Q(X) (with the Scott topology) of … Continue reading →

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