Abstract
Bornologies abstract the properties of bounded sets of a metric space. But there are unbounded bornologies on a metric space like $\mathcal{P}(\RR)$ with the Euclidean metric. We show that by replacing $[0,\infty)$ with a partially ordered monoid every bornology is the set of bounded subsets of a generalized metric mapped into a partially ordered monoid. We also prove that the set of bornologies on a set is the join completion of the equivalence classes of a relation on the power set of the set.
Publisher
Universitat Politecnica de Valencia
Reference39 articles.
1. M. Abel and A. Šostak, Towards the theory of L-bornological spaces, Iran. J. Fuzzy Syst. 8, no. 1 (2011), 19-28.
2. B. Banaschewski, Hüllensysteme und Erweiterung von Quasi-Ordnungen, Z. Math. Logik Grundlagen Math. 2 (1956), 35-46.
3. https://doi.org/10.1002/malq.19560020803
4. G. Beer, On metric boundedness structures, Set-valued Anal 7 (1999), 195-208.
5. https://doi.org/10.1023/A:1008720619545