The strong Whitney convergence on bornology introduced by Caserta in [9] is a
generalization of the strong uniform convergence on bornology introduced by
Beer-Levi in [5]. 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?chet property of these
spaces. In the process, we also present a new characterization for a
bornology to be shielded from closed sets.