Bornological modifications of hyperspace topologies

TL;DR

This paper explores bornological convergence structures on hyperspaces, characterizing their topological reflections and extending these concepts to a wider range of hyperspace topologies.

Contribution

It provides a characterization of topological reflections of bornological convergence pretopologies and generalizes the constructions to other hyperspace topologies.

Findings

Characterization of topological reflections of bornological convergence pretopologies

Extension of bornological convergence constructions to broader hyperspace topologies

Framework for analyzing bornological modifications in hyperspace topologies

Abstract

The bornological convergence structures that have been studied recently as generalizations of Attouch-Wets convergence define pretopologies on hyperspaces. In this paper we characterize the topological reflections of these pretopologies and translate the constructions necessary to define bornological convergence to a broader spectrum of hyperspace topologies.