Representations of bornologies




bornology, metrizablity, frame


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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How to Cite

H. Pajoohesh, “Representations of bornologies”, Appl. Gen. Topol., vol. 23, no. 1, pp. 17–30, Apr. 2022.