Prasenjit Bal†
This paper presents a comprehensive characterization of Menger spaces and star-Menger spaces through the lens of families of closed sets, employing nuanced modifications of the classical finite intersection property. By introducing and analyzing specific intersection patterns within these families, we develop conditions that encapsulate the essence of the Menger and star-Menger covering properties. Furthermore, we explore the associated selection principles and demonstrate how they can be systematically reversed to reconstruct the topological structure of Menger and star-Menger spaces. This dual perspective not only offers an alternative viewpoint on classical results but also contributes to the ongoing effort to bridge the gap between topological covering properties and combinatorial selection theory. Our results provide a new framework that enhances the theoretical understanding of these spaces and may inspire further investigations into related classes of topological spaces.
Keywords: Menger Space, star-Menger Space, selection principles, finite intersection property.
MSC: 54D20, 54D30, 54D40.
DOI 10.56082/annalsarscimath.2025.2.115
† balprasenjit177@gmail.com, Department of Mathematics, ICFAI University Tripura, Kamalghat, 799210, India
PUBLISHED in Annals Academy of Romanian Scientists Series on Mathematics and Its Application, Volume 17 no 2, 2025
