On a certain star-\(K\) variant of a selection principle (Q6635544)

The study of selection principles and related games in set-theoretic topology has a well-established history. Following Scheepers' systematic investigation of selection principles and corresponding games in [\textit{M. Scheepers}, Topology Appl. 69, No. 1, 31--62 (1996; Zbl 0848.54018)], this area has gained significant importance and has become one of the most active fields of research.\N\NIn this paper, D. Chandra and N. Alam introduce and study the ``star-\(K\)-Scheepers property'', a star variation of selection principle \(U_{\mathrm{fin}}(\mathcal{O},\Omega)\), now commonly referred to as the Scheepers property, along with its corresponding game. Specifically, the authors examine the relationships between the game corresponding to the star-\(K\)-Scheepers property and other variants of the Scheepers' games. Additionally, they investigate the preservation of certain properties under specific topological operations and present several open problems.