Certain observations on selection principles from (a) Bornological viewpoint

Abstract

This article is a continuation of the study of bornological open covers and related selection principles in metric spaces done in (Chandra et al. 2020 [6]) using the idea of strong uniform convergence (Beer and Levi, 2009 [3]) on a bornology. Here we explore further ramifications, presenting characterizations of various selection principles related to certain classes of bornological covers using the Ramseyan partition relations, interactive results between the cardinalities of bornological bases and certain selection principles involving bornological covers which have not been studied before. Further, some new observations on the -Hurewicz property introduced in [6] and several results on the -Gerlits-Nagy property (which is introduced here following the seminal work of [9]) are presented.