Xiaojun Ruan ; Xiaoquan Xu - $SI_2$-quasicontinuous spaces

entics:10355 - Electronic Notes in Theoretical Informatics and Computer Science, March 21, 2023, Volume 2 - Proceedings of ISDT 9 - https://doi.org/10.46298/entics.10355
$SI_2$-quasicontinuous spacesArticle

Authors: Xiaojun Ruan ; Xiaoquan Xu

    In this paper, as a common generalization of $SI_{2}$-continuous spaces and $s_{2}$-quasicontinuous posets, we introduce the concepts of $SI_{2}$-quasicontinuous spaces and $\mathcal{GD}$-convergence of nets for arbitrary topological spaces by the cuts. Some characterizations of $SI_{2}$-quasicontinuity of spaces are given. The main results are: (1) a space is $SI_{2}$-quasicontinuous if and only if its weakly irreducible topology is hypercontinuous under inclusion order; (2) A $T_{0}$ space $X$ is $SI_{2}$-quasicontinuous if and only if the $\mathcal{GD}$-convergence in $X$ is topological.


    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,06B35, 06B75, 54F05

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