TITLE:
Some Classes of Bounded Sets in Quasi-Metric Spaces
AUTHORS:
Danny Mukonda, Levy Kahyata Matindih, Edwin Moyo
KEYWORDS:
Quasi-Metric-Boundedness, Totally Boundedness, Bourbaki Boundedness, Bornology
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.12 No.12,
December
8,
2022
ABSTRACT: 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.