On Bourbaki-bounded sets on quasi-pseudometric spaces
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2022
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Otafudu, Olivier Olela
Mukonda, Danny
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Mark
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Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky
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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.
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Mathematics for Applications. 2022 vol. 11, č. 2, s. 155-168. ISSN 1805-3629
http://ma.fme.vutbr.cz/archiv/11_2/mfa_11_2_otafudu_mukonda_final.pdf
http://ma.fme.vutbr.cz/archiv/11_2/mfa_11_2_otafudu_mukonda_final.pdf
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Peer-reviewed
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en
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© Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky