A memo on bornologies and size functions

TL;DR

This paper explores the concept of abstract bornologies and their relation to topological spaces and size functions, proposing a way to connect size functions with maxitive measures as a generalization of non-compactness measures.

Contribution

It introduces a framework linking bornologies, topological spaces, and size functions, and shows how size functions can be represented as maxitive measures.

Findings

Established a connection between size functions and maxitive measures.

Provided a generalized approach to measures of non-compactness.

Clarified the role of bornologies in topological analysis.

Abstract

We recall the notion of abstract bornology, and connect it with topological spaces and size functions. As a generalization of measures of non-compactness, we show how every size function can be mapped to a maxitive measure.