Certain observations on statistical variations of bornological covers

Abstract

We primarily make a general approach to the study of open covers and related selection principles using the idea of statistical convergence in metric space. In the process we are able to extend some results in (Caserta et al. 2012; Chandra et al. 2020) where bornological covers and related selection principles in metric spaces have been investigated using the idea of strong uniform convergence (Beer and Levi, 2009) on bornology. We introduce the notion of statistical-$\gamma_{\mathfrak{B}^s}$-cover, statistically-strong-$\mathfrak{B}$-Hurewicz and statistically-strong-$\mathfrak{B}$-groupable cover and study some of its properties mainly related to the selection principles and corresponding games. Also some properties like statistically-strictly Fr\`{e}chet Urysohn, statistically-Reznichenko property and countable fan tightness have also been investigated in $C(X)$ with respect to the topology of strong uniform convergence $\tau^s_\mathfrak{B}$.