Complete metrizability of the topology of strong Whitney convergence on bornology

Abstract

The topology of strong Whitney convergence on bornology was introduced by Caserta in \cite{MR3086688}. This paper studies the complete metrizability of the space of all real-valued continuous functions on a metric space, equipped with the topologies of Whitney and strong Whitney convergence on bornology. The Polishness of these topologies coincides with their complete metrizability.