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math.LO2026
Scott topologies on meet-continuous domains
Xiaoquan Xu
We study Scott products and sobriety of countable meet-continuous domains, meaning meet-continuous dcpos without any additional continuity or least-element assumption. Using the co…
math.LO2026
Every countable meet-continuous lattice is Scott sober
Xiaoquan Xu, Wei Ji
We prove that every countable meet-continuous lattice is Scott sober. For any family of such lattices, the Scott topology on the product equals the product of the factor Scott topo…