Star versions of Hurewicz spaces

Authors : Sumit SİNGH, Ljubiša D. R. KOČİNAC

Pages : 1325-1333

Doi:10.15672/hujms.819719

View : 9 | Download : 9

Publication Date : 2021-10-15

Article Type : Research Paper

Abstract :A space $X$ is said to have the set star Hurewicz property if for each nonempty subset $A$ of $X$ and each sequence $insert ignore into journalissuearticles values(\mathcal{U}_n: n\in \mathbb{N});$ of collections of sets open in $X$ such that for each $n\in \mathbb N$, $\overline{A} \subset \cup \mathcal{U}_n$, there is a sequence $insert ignore into journalissuearticles values(\mathcal{V}_n: n \in \mathbb{N});$ such that for each $n \in \mathbb{N}$, $\mathcal{V}_n$ is a finite subset of $\mathcal{U}_n$ and for each $x \in A$, $x \in {\rm St}insert ignore into journalissuearticles values(\cup\mathcal{V}_n, \mathcal{U}_n);$ 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.
Keywords : Hurewicz, star Hurewicz, strongly star Hurewicz, set star Hurewicz, set SSH