Some characterizations of ideal variants of Hurewicz type covering properties

TL;DR

This paper explores various ideal-based Hurewicz covering properties in topology, providing characterizations through basis, measure zero, and selection principles, especially for metrizable spaces.

Contribution

It introduces new characterizations of ideal Hurewicz properties using basis, measure zero, and selection principles, advancing understanding of these topological covering properties.

Findings

Characterized $ ext{I}$-Hurewicz property via basis and measure zero.

Connected star-$ ext{I}$-Hurewicz properties with selection principles.

Extended characterizations to metrizable spaces.

Abstract

In this paper, we continue to investigate topological properties of $\mathcal{I}H$ and its two star versions namely $SS \mathcal{I} H$ and $S \mathcal{I} H$. We characterized $\mathcal{I}$-Hurewicz property by $\mathcal{I}$-Hurewicz Basis property and $\mathcal{I}$-Hurewicz measure zero property for metrizable spaces. We also characterized $\mathcal{I}$-Hurewicz property, star-$\mathcal{I}$-Hurewicz property and strongly star-$\mathcal{I}$-Hurewicz property using selection principles.