Bornologies and filters in selection principles on function spaces

We extend known results of selection principles in $C_p$-theory to the context of spaces of the form $C_{\mathcal{B}}(X)$, where $\mathcal{B}$ is a bornology on $X$. Particularly, by using the filter approach of Jordan to $C_p$-theory, we show that $\gamma$-productive spaces are productive with a larger class of $\gamma$-like spaces.