On star Rothberger spaces modulo an ideal (Q6640027)

A topological space \(X\) is Rothberger if for every sequence of open covers of \(X\) there exists a sequence composed of members of each of these coverings such that it covers \(X\). \textit{M. Sakai} [Topology Appl. 176, 22--34 (2014; Zbl 1298.54015)] studied some of weaker form of this concept, as star Rothberger. Recently \textit{A. Güldürdek} [Hacet. J. Math. Stat. 47, No. 1, 69--75 (2018; Zbl 1397.54034)] and \textit{M. Bhardwaj} [ibid. 50, No. 1, 144--145 (2021; Zbl 1488.54073)] have started some investigations on the ideal versions of Rothberger spaces.\N\NIn this paper, the authors introduce the ideal star Rothberger property by coupling the notion of a star operator to that of an ideal Rothberger space, after which some of its topological characteristics are analyzed. By creating relationships between a numbers of topological features with structures similar to the ideal star Rothberger space, they reinforce the concept. In order to illustrate the diferences between a number of related topological properties, they also provide several counterexamples. Certain preservation-related properties under subspaces and functions are investigated. Lastly they find a way to express ideal star Rothberger space by means of families of closed sets.