Selection principles and weaker forms of Menger, Rothberger and Hurewicz Properties in Topology

Abstract

In this research work, our focus is to study certain covering properties in topological spaces by using semiopen covers and in bitopological spaces by using pairwise open covers and their generalizations. This work deals with Menger type, Rothberger type and Hurewicz type covering properties. The notions of semiMenger (semiRothberger), almost semiMenger (almost semiRothberger), star semiMenger (star semiRothberger), almost star semiMenger (almost star semiRothberger) and strongly star semiMenger (strongly star semiRothberger) are defined and corresponding covering properties are investigated. Furthermore, the concepts of semiHurewicz, almost semiHurewicz and star semiHurewicz spaces are introduced and their properties are studied. Relations between the newly defined notions and classical selection principles are established. Similarities and differences among each other are discussed. We have also studied the prototypes of some selection principles using p-open covers in bitopological spaces.