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Some Classes of Bounded Sets in Quasi-Metric Spaces
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作者 Danny Mukonda Levy Kahyata Matindih Edwin Moyo 《Advances in Pure Mathematics》 2022年第12期701-714,共14页
This note deals with some classes of bounded subsets in a quasi-metric space. We study and compare the bounded sets, totally-bounded sets and the Bourbaki-bounded sets on quasi metric spaces. For example, we show that... This note deals with some classes of bounded subsets in a quasi-metric space. We study and compare the bounded sets, totally-bounded sets and the Bourbaki-bounded sets on quasi metric spaces. For example, we show that in a quasi-metric space, a set may be bounded but not totally bounded. In addition, we investigate their bornologies as well as their relationships with each other. For example, given a compatible quasi-metric, we intend to give some necessary and sufficient conditions for which a quasi metric bornology coincides with the bornology of totally bounded sets, the bornology of bourbaki bounded sets and bornology of bourbaki bounded subsets. 展开更多
关键词 Quasi-Metric-boundedness Totally boundedness bourbaki boundedness BORNOLOGY
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