Products of two sober dcpo's need not be sober
General Topology
2025-12-23 v4
Abstract
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. Meantime, we show that if and are special type of sober complete lattices, then the Scott space of their order product is sober.
Cite
@article{arxiv.2408.08587,
title = {Products of two sober dcpo's need not be sober},
author = {Hualin Miao and Xiaoyong Xi and Xiaodong Jia and Qingguo Li and Dongsheng Zhao},
journal= {arXiv preprint arXiv:2408.08587},
year = {2025}
}
Comments
Typo corrections