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Some classes of bounded sets in metric spaces


Garrido, M. Isabel and Meroño, Ana Soledad (2012) Some classes of bounded sets in metric spaces. In Contribuciones matemáticas en honor a Juan Tarrés. UCM, Madrid, pp. 179-186. ISBN 978-84-695-4421-1


This note deals with some classes of bounded subsets in a metric space. Namely, sets of finite diameter, totally-bounded sets and the so-called Bourbaki-bounded sets. We will see some good and some bad properties of each class, as well as their relationships. A more detailed study about Bourbaki-boundedness is also presented. Finally a new property of completeness in metric spaces is introduced, which we call Bourbaki-completeness.

Item Type:Book Section
Uncontrolled Keywords:Metric-bounded; Totally bounded; Bourbaki-bounded; Bourbaki-complete
Subjects:Sciences > Mathematics > Geometry
Sciences > Mathematics > Topology
ID Code:17374
Deposited On:11 Dec 2012 10:35
Last Modified:27 May 2016 14:40

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