Hualin Miao ; Qingguo Li ; Dongsheng Zhao - One-step closure, weak one-step closure and meet continuity

entics:10352 - Electronic Notes in Theoretical Informatics and Computer Science, March 21, 2023, Volume 2 - Proceedings of ISDT 9 - https://doi.org/10.46298/entics.10352
One-step closure, weak one-step closure and meet continuityArticle

Authors: Hualin Miao ; Qingguo Li ; Dongsheng Zhao

    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.


    Volume: Volume 2 - Proceedings of ISDT 9
    Published on: March 21, 2023
    Accepted on: November 25, 2022
    Submitted on: November 23, 2022
    Keywords: Mathematics - General Topology

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