Tag Archives: Hoare hyperspace

When is ℒ(X) locally compact?

Posted on November 21, 2024 by jgl

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 , , , , | Comments Off on When is ℒ(X) locally compact?

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 →

Posted in Uncategorized | Tagged , , , , , | Comments Off on On products of dcpos, the Miao-Xi-Li-Zhao lemma, and the complete lattice Lfan (part I)

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 →

Posted in Uncategorized | Tagged , , , , , | Comments Off on Compact semilattices without small semilattices I: interval homomorphisms, products, and the Hoare hyperspace