Mengjie Jin ; Qingguo Li - On $k$-ranks of topological spaces

entics:10349 - Electronic Notes in Theoretical Informatics and Computer Science, March 21, 2023, Volume 2 - Proceedings of ISDT 9 - https://doi.org/10.46298/entics.10349
On $k$-ranks of topological spacesArticle

Authors: Mengjie Jin ; Qingguo Li

    In this paper, the concepts of $K$-subset systems and $k$-well-filtered spaces are introduced, which provide another uniform approach to $d$-spaces, $s$-well-filtered spaces (i.e., $\mathcal{U}_{S}$-admissibility) and well-filtered spaces. We prove that the $k$-well-filtered reflection of any $T_{0}$ space exists. Meanwhile, we propose the definition of $k$-rank, which is an ordinal that measures how many steps from a $T_{0}$ space to a $k$-well-filtered space. Moreover, we derive that for any ordinal $\alpha$, there exists a $T_{0}$ space whose $k$-rank equals to $\alpha$. One immediate corollary is that for any ordinal $\alpha$, there exists a $T_{0}$ space whose $d$-rank (respectively, $wf$-rank) equals to $\alpha$.


    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,54H99

    Consultation statistics

    This page has been seen 105 times.
    This article's PDF has been downloaded 57 times.