Strong Whitney Convergence on Bornologies

Abstract

The strong Whitney convergence on bornology introduced by Caserta in [Strong Whitney convergence, Filomat, 26:1 (2012), 81-91] is a generalization of the strong uniform convergence on bornology introduced by Beer-Levi in [Strong uniform continuity, J. Math. Anal. Appl., 350 (2009), 568-589].
This paper aims to study some important topological properties of the space of all real valued continuous functions on a metric space endowed with the topologies of Whitney and strong Whitney convergence on bornology. More precisely, we investigate metrizability, various countability properties, countable tightness, and Fr\'{e}chet property of these spaces. In the process, we also present a new characterization for a bornology to be shielded from closed sets.