One-step closure, weak one-step closure and meet continuity
General Topology
2023-06-22 v2
Abstract
This paper studies the weak one-step closure and one-step closure properties concerning the structure of Scott closures. We deduce that every quasicontinuous domain has weak one-step closure and show that a quasicontinuous poset need not have weak one-step closure. We also constructed a non-continuous poset with one-step closure, which gives a negative answer to an open problem posed by Zou et al.. Finally, we investigate the relationship between weak one-step closure property and one-step closure property and prove that a poset has one-step closure if and only if it is meet continuous and has weak one-step closure.
Cite
@article{arxiv.2211.10106,
title = {One-step closure, weak one-step closure and meet continuity},
author = {Hualin Miao and Qingguo Li and Dongsheng Zhao},
journal= {arXiv preprint arXiv:2211.10106},
year = {2023}
}