Abstract: The statistical convergence in a topological space is constrained in this study up to order \alpha, where \alpha \in (0, 1). A fresh group of open covers (namely s^{\alpha}-\gamma covers) and an entirely novel category of denseness (namely s^{\alpha}-denseness) are proposed using this notion of s^{\alpha}-convergence, which has been used to study various topological aspects of s^{\alpha}-density. It has been revealed that the class of s^{\alpha}-\gamma coverings falls somewhere between the class of \gamma covers and the class of s-\gamma~covers. The influence of s^{\alpha}-\gamma covers in topological games and selection principles are also investigated.
Keywords: asymptotic density; statistical convergence; \gamma cover; selection principle
DOI: DOI 10.14712/1213-7243.2025.010
AMS Subject Classification: 54D20 54B20 54C35