Bornologies and filters in selection principles on function spaces

TL;DR

This paper extends selection principles in $C_p$-theory to spaces of the form $C_{eta}(X)$ with bornologies, using filters to show broader productivity results for $b3$-like spaces.

Contribution

It generalizes known results by incorporating bornologies and filter methods, broadening the class of spaces with productive properties in $C_p$-theory.

Findings

$b3$-productive spaces are productive with a larger class of $b3$-like spaces

Extension of selection principles to $C_{eta}(X)$ spaces with bornologies

Application of Jordan's filter approach to $C_p$-theory

Abstract

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.