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math.GN2025
Products of two sober dcpo's need not be sober
Hualin Miao, Xiaoyong Xi, Xiaodong Jia +2
We construct two dcpo's whose Scott spaces are sober, but the Scott space of their order product is not sober. This answers an open problem on the sobriety of Scott spaces. Meantim…
math.GN2025
Posets uniquely determined by its compact saturated subsets
Huijun Hou, Qingguo Li
Inspired by Zhao and Xu's study on which a dcpo can be determined by its Scott closed subsets lattice, we further investigate whether a poset (or dcpo) is able to be determined…
math.GN2024
-well-filtered spaces, revisited
Hualin Miao, Xiaodong Jia, Ao Shen +1
We prove that a topological space is -well-filtered if and only if it does not admit either the natural numbers with the cofinite topology or with the Scott topology as i…