Applications of bornological covering properties in metric spaces

摘要

Using the idea of strong uniform convergence (Beer and Levi, 2009; Caserta et al., 2010) on bornology, Caserta et al. (2012) studied open covers and selection principles in the realm of metric spaces (associated with a bornology) and function spaces (w.r.t. the topology of strong uniform convergence). We primarily continue in the line initiated in Caserta et al. (2012) and investigate the behaviour of various selection principles related to these classes of bornological covers. In the process we obtain implications among these selection principles resulting in Scheepers' like diagrams. We also introduce the notion of strong-B-Hurewicz property and investigate some of its consequences. Finally, in C(X) with respect to the topology tau(s)(B) of strong uniform convergence, important properties like countable T-tightness, Reznichenko property are characterized in terms of bornological covering properties of X. (C) 2019 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.