On Bourbaki-bounded sets on quasi-pseudometric spaces
| dc.contributor.author | Otafudu, Olivier Olela | |
| dc.contributor.author | Mukonda, Danny | |
| dc.coverage.issue | 2 | cs |
| dc.coverage.volume | 11 | cs |
| dc.date.accessioned | 2023-01-02T07:54:45Z | |
| dc.date.available | 2023-01-02T07:54:45Z | |
| dc.date.issued | 2022 | cs |
| dc.description.abstract | In metric spaces, a set is Bourbaki-bounded if and only if every real- valued uniformily continuous function on it is bounded. In this article, we study Bourbaki-boundedness on quasi-pseudometric spaces. It turns out that if a set is Bourbaki-bounded on a symmetrized quasi-pseudometric space, then it is Bourbaki- bounded in the quasi-metric space but the converse need not to be true. We show that an asymmetric normed space is Bourbaki-bounded if and only if it is bounded. Consequently, we prove that every real-valued semi-Lipschitz in the small function on a quasi-metric space is bounded if and only if the quasi-metric is Bourbaki-bounded. This article extends some results from Beer and Garrido’s paper [2] from the metric point of view to the context of quasi-metric spaces. | en |
| dc.format | text | cs |
| dc.format.extent | 155-168 | cs |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.citation | Mathematics for Applications. 2022 vol. 11, č. 2, s. 155-168. ISSN 1805-3629 | cs |
| dc.identifier.doi | 10.13164/ma.2022.12 | en |
| dc.identifier.issn | 1805-3629 | |
| dc.identifier.uri | http://hdl.handle.net/11012/208724 | |
| dc.language.iso | en | cs |
| dc.publisher | Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky | cs |
| dc.relation.ispartof | Mathematics for Applications | en |
| dc.relation.uri | http://ma.fme.vutbr.cz/archiv/11_2/mfa_11_2_otafudu_mukonda_final.pdf | cs |
| dc.rights | © Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky | cs |
| dc.rights.access | openAccess | en |
| dc.subject | bornology, Bourbaki-boundedness, semi-Lipschitz, continuity | en |
| dc.title | On Bourbaki-bounded sets on quasi-pseudometric spaces | en |
| dc.type.driver | article | en |
| dc.type.status | Peer-reviewed | en |
| dc.type.version | publishedVersion | en |
| eprints.affiliatedInstitution.department | Ústav matematiky | cs |
| eprints.affiliatedInstitution.faculty | Fakulta strojního inženýrství | cs |
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