Topologies of (strong) uniform convergence on bornologies

TL;DR

This paper investigates the properties of topologies of strong uniform convergence on bornologies, focusing on cardinal invariants and generalizing existing results in the context of continuous real-valued functions.

Contribution

It advances the understanding of these topologies by analyzing cardinal invariants and extending previous findings in the field.

Findings

Determined cardinal invariants for these topologies.

Generalized known results to broader classes of bornologies.

Provided new insights into the structure of function spaces.

Abstract

We continue the study of topologies of strong uniform convergence on bornologies initiated in [G. Beer and S. Levi, Strong uniform continuity, J. Math Anal. Appl., 350:568-589, 2009] and [G. Beer and S. Levi, Uniform continuity, uniform convergence and shields, Set-Valued and Variational Analysis, 18:251-275, 2010]. We study cardinal invariants of topologies of (strong) uniform convergence on bornologies on the space of continuous real-valued functions and we also generalize some known results from the literature.