3 papers
math.CT2026
Commutation of Smyth and Hoare Power Constructions in Well-filtered Dcpos
Huijun Hou, Qingguo Li
Prior work [11] established a commutativity result for the Hoare power construction and a modified version of the Smyth power construction consisting of strongly compact sets, whic…
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…