Hurewicz空间的星型
Star versions of Hurewicz spaces
摘要：
一个空间$X$被称为具有集星Hurewicz性质，如果对于$X$的每个非空子集$A$和$X$中开集的每个序列$(\mathcal{U}_n: n \in \mathbb{N})$，使得对于每个$n\in \mathbb N$，$\overline{A} \subset \cup \mathcal{U}_n$，有一个序列$(\mathcal{V}_n: n \in \mathbb{N})$，使得对于每个$n \in \mathbb{N}$，$\mathcal{V}_n$是$\mathcal{U}_n$的有限子集，对于每个$x \in A$，$x \in {\rm St}(\cup \mathcal{V}_n, \mathcal{U}_n)$对于除了100个$n$之外的所有$n$。本文研究了集星Hurewicz、集强星Hurewicz与其它相关覆盖性质之间的关系，并研究了这些拓扑空间的拓扑性质.
英文摘要：
A space $X$ is said to have the set star Hurewicz property if for each nonempty subset $A$ of $X$ and each sequence $(\mathcal{U}_n: n \in \mathbb{N})$ of sets open in $X$ such that for each $n\in \mathbb N$, $\overline{A} \subset \cup \mathcal{U}_n$, there is a sequence $(\mathcal{V}_n: n \in \mathbb{N})$ such that for each $n \in \mathbb{N}$, $\mathcal{V}_n$ is a finite subset of $\mathcal{U}_n$ and for each $x \in A$, $x \in {\rm St}(\cup \mathcal{V}_n, \mathcal{U}_n)$ for all but finitely many $n$. In this paper, we investigate the relationships among set star Hurewicz, set strongly star Hurewicz and other related covering properties and study the topological properties of these topological spaces.
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