Representations of bornologies | Zendy

Homeira Pajoohesh | Zendy

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Representations of bornologies

Author(s) -

Homeira Pajoohesh

Publication year - 2022

Publication title -

applied general topology

Language(s) - English

Resource type - Journals

eISSN - 1989-4147

pISSN - 1576-9402

DOI - 10.4995/agt.2022.16405

Subject(s) - mathematics , monoid , metric space , bounded function , equivalence relation , metric (unit) , equivalence (formal languages) , set (abstract data type) , combinatorics , euclidean space , discrete mathematics , power set , mathematical analysis , computer science , operations management , economics , programming language

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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