Tag Archives: hyperspace

Strongly compact sets and the double hyperspace construction

Posted on October 19, 2022 by jgl

The notion of strongly compact set is due to Reinhold Heckmann. A few months ago, I said that I would explain why the sobrification of the space Qfin(X) of finitary compact sets on a sober space X is not the … Continue reading →

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Topological lattices with small semilattices

Posted on April 19, 2022 by jgl

I would like to explain a clever counterexample due to Jimmie Lawson in 1970, or rather a slight variant of it, pertaining to the theory of topological semilattices and to a property that crops up naturally, namely having small semilattices. … 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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Irredundant families, the Smyth powerdomain, the Lyu-Jia theorem, and the baby Groemer theorem

Posted on January 20, 2022 by jgl

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 →

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