Huijun Hou ; Qingguo Li - Weakly meet $s_{Z}$-continuity and $\delta_{Z}$-continuity

entics:10344 - Electronic Notes in Theoretical Informatics and Computer Science, March 21, 2023, Volume 2 - Proceedings of ISDT 9 - https://doi.org/10.46298/entics.10344
Weakly meet $s_{Z}$-continuity and $\delta_{Z}$-continuityArticle

Authors: Huijun Hou ; Qingguo Li

    Based on the concept of weakly meet $s_{Z}$-continuouity put forward by Xu and Luo in \cite{qzm}, we further prove that if the subset system $Z$ satisfies certain conditions, a poset is $s_{Z}$-continuous if and only if it is weakly meet $s_{Z}$-continuous and $s_{Z}$-quasicontinuous, which improves a related result given by Ruan and Xu in \cite{sz}. Meanwhile, we provide a characterization for the poset to be weakly meet $s_{Z}$-continuous, that is, a poset with a lower hereditary $Z$-Scott topology is weakly meet $s_{Z}$-continuous if and only if it is locally weakly meet $s_{Z}$-continuous. In addition, we introduce a monad on the new category $\mathbf{POSET_{\delta}}$ and characterize its $Eilenberg$-$Moore$ algebras concretely.


    Volume: Volume 2 - Proceedings of ISDT 9
    Published on: March 21, 2023
    Accepted on: November 22, 2022
    Submitted on: November 22, 2022
    Keywords: Mathematics - General Topology,06A06 (Primary) 18C15, 18C20 (Secondary)

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