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- W4328130005 abstract "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 $alpha$." @default.
- W4328130005 created "2023-03-22" @default.
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- W4328130005 date "2023-03-21" @default.
- W4328130005 modified "2023-10-05" @default.
- W4328130005 title "On $k$-ranks of topological spaces" @default.
- W4328130005 doi "https://doi.org/10.46298/entics.10349" @default.
- W4328130005 hasPublicationYear "2023" @default.
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