Unification of relative versions of some star-covering properties

Abstract

In this paper, we introduce relative star-∆ -Menger property in topological spaces following the approach of Bonanzinga and Pansera (Acta Math. Hungar. 117 (3) 231– 243, 2007), which unifies the relative versions of star-K -Menger property, star-C - Menger property and star-L -Menger property in the same. We then study the properties of such spaces and also its relationships with different types of existing Menger properties present in the literature. Finally, we study the preservation properties of such spaces and discuss about the associated star-∆ -Menger game.