Representations of bornologies

Homeira Pajoohesh

doi:10.4995/agt.2022.16405

Authors

Homeira Pajoohesh Medgar Evers College https://orcid.org/0000-0003-4035-0032

DOI:

https://doi.org/10.4995/agt.2022.16405

Keywords:

bornology, metrizablity, frame

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.

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