On certain star-$K$ variant of a selection principle

Abstract

This article deals with certain star variants of the Scheepers property. We introduce and study the star-$K$-Scheepers property and corresponding game. The relationships between the game corresponding to the star-$K$-Scheepers property and other variants of the Scheepers games are investigated. Furthermore, the relation among the winning strategies of the players in such games are represented in an implication diagram. We present certain observations in terms of Alster covers and the Alexandroff duplicates. In addition, we examine few preservation like properties in this context. Some open problems are also posed.