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math.LO2026
Scott products and sobriety of countable meet-continuous dcpos
Xiaoquan Xu, Wei Ji
We study Scott-product compatibility and sobriety for countable meet-continuous directed-complete partial orders (dcpos). We construct a countable meet-continuous dcpo …
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…