Some remarks on open covers and selection principles using ideals

Abstract

In this paper we follow the line of recent works of Das [4,5,7] (see also [3] for similar investigation), where a more general approach was made to study certain results on open covers and selection principles by using the notion of ideals and ideal convergence, which automatically extends similar classical results (where finite sets are used), and also recent statistical variants studied by Di Maio and Kočinac [10]. Here we further introduce the notions of cω-covers and I-large covers which extend the notions of ω-covers and large covers in a topological space. We then study the I-groupability of different open covers and some of its consequences.