An ideal version of star-C-Hurewicz covering property

Abstract

A space X is said to have star-C-$ \mathcal{I} $-Hurewicz (SC$ \mathcal{I} $H)  property   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 countably 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} $. In this paper, we introduced the ideal versions of star-C-Hurewicz (SCH)  property called SC$ \mathcal{I} $H. We investigated the relationships among SC$ \mathcal{I} $H and related properties and studied the topological properties of SC$ \mathcal{I} $H property. Our results and examples extend and  improved some earlier results from \cite{SYKCH,SYKCM} and present a more general version with respect to ideals.