Bornologies and bitopological function spaces

The aim of this paper is to study certain closure-type properties of function spaces over metric spaces endowed with two topologies: the topology of uniform convergence on a bornology and the topology of strong uniform convergence on a bornology. The study of function spaces with the strong uniform topology on a bornology was initiated by G. Beer and S. Levi in 2009, and then continued by several authors: A. Caserta, G. Di Maio and L'. Holáa in 2010, A. Caserta, G. Di Maio, Lj.D.R. Kočcinac in 2012. Properties that we consider in this paper are defined in terms of selection principles.