On star-K-$ \mathcal{I} $-Hurewicz property

Abstract

A space X is said to have the star-K-$ \mathcal{I} $-Hurewicz property (SK$ \mathcal{I} $H) \cite{TSM} if for each sequence $ (\mathcal{U}_n: n \in \mathbb{N}) $ of open covers of X there is a sequence $ (K_n: n \in \mathbb{N}) $ of compact subsets of X such that for each $ x \in X $, $ \{n \in \mathbb{N}: x \notin  St(K_n, \mathcal{U}_n) \} \in \mathcal{I}$, where  $ \mathcal{I} $ is the proper admissible ideal of $ \mathbb{N} $. In this paper, we continue to investigate the relationship between the SK$ \mathcal{I} $H property and other related properties and study the topological properties of the SK$ \mathcal{I} $H property.