The topology of strong Whitney convergence on bornology was introduced by Caserta in 6. This paper studies the complete metrizability and several other completeness properties 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.
Ajay Kumawat (Wed,) studied this question.