论文标题
在$ k $ lanks上的拓扑空间
On $k$-ranks of topological spaces
论文作者
论文摘要
在本文中，介绍了$ k $ - subset系统和$ k $过滤的空间的概念，这为$ d $ spaces，$ s $ well滤波器的空间提供了另一种统一的方法（即，$ \ nathcal {u} _ {u} _ {s} _ {s} $ - 可靠性），并得到了充实的空间。我们证明，存在任何$ t_ {0} $ space的$ k $过滤反射。同时，我们提出了$ k $ -rank的定义，该定义是一个序数，可衡量从$ t_ {0} $ space到$ k $过滤的空间的几个步骤。此外，我们得出的是，对于任何有序$α$，都存在$ t_ {0} $ space，其$ k $ -rank等于$α$。一个即时的推论是，对于任何列出的$α$，存在$ t_ {0} $ space，其$ d $ -rank（分别为$ wf $ -rank）等于$α$。
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 $α$, there exists a $T_{0}$ space whose $k$-rank equals to $α$. One immediate corollary is that for any ordinal $α$, there exists a $T_{0}$ space whose $d$-rank (respectively, $wf$-rank) equals to $α$.
