Star versions of Hurewicz spaces

Year 2021, Volume: 50 Issue: 5, 1325 - 1333, 15.10.2021

Sumit Singh , Ljubiša D. R. Kočinac

https://doi.org/10.15672/hujms.819719

Cited By: 9

Abstract

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 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 $(\mathcal{V}_n: n \in \mathbb{N})$ 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.

Keywords

Hurewicz , star-Hurewicz , strongly star-Hurewicz , set star Hurewicz , set-SSH

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