Bornologies, selection principles and function spaces

TL;DR

This paper investigates the closure properties of certain function spaces with a new topology based on bornologies, focusing on their relation to selection principles.

Contribution

It introduces and analyzes the closure-type properties of function spaces with a novel topology of strong uniform convergence on bornologies, extending prior work.

Findings

Identifies specific closure properties of these function spaces.

Links the properties to selection principles in topology.

Builds on and extends previous studies from 2009 and later works.

Abstract

We study some closure-type properties of function spaces endowed with the new topology of strong uniform convergence on a bornology introduced by Beer and Levy in 2009. The study of these function spaces was initiated in [2] and [3]. The properties we study are related to selection principles.