Some observations on ideal variations of bornological covers

Abstract

In this article, we use the notion of ideals to study  open covers and related selection principles, and thus, we extend some results in (Caserta et al. 2012; Chandra et~al. 2020) where open covers and related selection principles have been investigated using the idea of strong uniform convergence (Beer and Levi, 2009) on a bornology. We introduce the notions of $\ic$-$\gamma_{\mathfrak{B}^s}$-cover, $\ic$-strong-$\mathfrak{B}$\discretionary{-}{-}{-}Hurewicz and $\ic$-strong-$\mathfrak{B}$-groupable cover.
Also, in $\bl(C(X), \tau^s_\mathfrak{B}\br)$, some properties like $\ic$-strictly Fr\`{e}chet Urysohn, $\ic$-Reznichenko property are investigated.