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arXiv · 2211.10106

One-step closure, weak one-step closure and meet continuity

Hualin Miao·Qingguo Li·Dongsheng Zhao
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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.

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Hualin Miao, Qingguo Li, Dongsheng Zhao. 2022-11-18. One-step closure, weak one-step closure and meet continuity. https://doi.org/10.46298/entics.10352

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