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math.GN2026
A note on power spaces and function spaces of strongly well-filtered spaces
Zhenzhu Yuan, Xiangrui Li, Bei Liu +1
Strong well-filteredness is a refinement of well-filteredness arising naturally in non-Hausdorff topology and domain theory. In this paper, we construct a countable locally compact…
math.GN2026
Co-Noetherian spaces
Xiangrui Li, Qingguo Li
In non-Hausdorff topology, many spaces exhibit significant separation properties, such as sober spaces, well-filtered spaces and d-spaces. These properties serve to fundamentally c…
math.GN2025
Sober topologies on a set
Xiangrui Li, Qingguo Li, Dongsheng Zhao
The collection of all topologies on a set X forms a complete lattice with respect to the inclusion order, which have been investigated by many researchers. Sobriety is one of the c…