Representations of bornologies
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 g...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Universitat Politècnica de València
2022-04-01
|
| Series: | Applied General Topology |
| Subjects: | |
| Online Access: | https://polipapers.upv.es/index.php/AGT/article/view/16405 |
| _version_ | 1811328549969199104 |
|---|---|
| author | Homeira Pajoohesh |
| author_facet | Homeira Pajoohesh |
| author_sort | Homeira Pajoohesh |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-13T15:27:05Z |
| format | Article |
| id | doaj.art-b91bbfccc75c44da905f4b7cc735344c |
| institution | Directory Open Access Journal |
| issn | 1576-9402 1989-4147 |
| language | English |
| last_indexed | 2024-04-13T15:27:05Z |
| publishDate | 2022-04-01 |
| publisher | Universitat Politècnica de València |
| record_format | Article |
| series | Applied General Topology |
| spelling | doaj.art-b91bbfccc75c44da905f4b7cc735344c2022-12-22T02:41:29ZengUniversitat Politècnica de ValènciaApplied General Topology1576-94021989-41472022-04-01231173010.4995/agt.2022.1640513481Representations of bornologiesHomeira Pajoohesh0https://orcid.org/0000-0003-4035-0032Medgar Evers CollegeBornologies 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.https://polipapers.upv.es/index.php/AGT/article/view/16405bornologymetrizablityframe |
| spellingShingle | Homeira Pajoohesh Representations of bornologies Applied General Topology bornology metrizablity frame |
| title | Representations of bornologies |
| title_full | Representations of bornologies |
| title_fullStr | Representations of bornologies |
| title_full_unstemmed | Representations of bornologies |
| title_short | Representations of bornologies |
| title_sort | representations of bornologies |
| topic | bornology metrizablity frame |
| url | https://polipapers.upv.es/index.php/AGT/article/view/16405 |
| work_keys_str_mv | AT homeirapajoohesh representationsofbornologies |