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

TL;DR

This paper introduces and investigates the star-$K$-Scheepers property and its associated game, exploring their relationships with other variants, strategies, and preservation properties within topological selection principles.

Contribution

It defines the star-$K$-Scheepers property, studies its game-theoretic aspects, and explores relationships with existing variants, providing new insights and open problems.

Findings

Relationships between star-$K$-Scheepers and other variants established

Implication diagram of winning strategies created

Observations made using Alster covers and Alexandroff duplicates

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.