2 papers
math.GN2026
Sobriety of Scott topologies under countability conditions
Zhengmao He, Zhaochen Dong, Kaiyun Wang
In this paper, we focus on the sobriety of the Scott topology in countable case. Specifically, we show that: (1) every meet-continuous core-compact countable dcpo is sober with res…
math.CO2026
The Kelly--Trotter product conjecture for posets of dimension three
Zhaochen Dong, Kaiyun Wang
Kelly and Trotter conjectured that dim(P x Q) >= dim P + dim Q - 2 for all finite posets P and Q. We prove the conjecture when dim P = dim Q = 3. This also disproves Trotter's conj…