Tag Archives: semilattice

Compact semilattices without small semilattices I: interval homomorphisms, products, and the Hoare hyperspace

Posted on October 20, 2023 by jgl

I have already talked about compact semilattices before, but there is a lot more to say, especially on the subject of having small semilattices or not. Zhenchao Lyu is joining me this month, and we will pursue this next month. … Continue reading →

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The fundamental theorem of compact semilattices

Posted on August 20, 2023 by jgl

Bounded-complete domains, or bc-domains, are an amazingly rich kind of continuous domains. They form a Cartesian-closed category, and they are the densely injective topological spaces, among other properties. One characterization of bc-domains which I have not included in the book … 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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