Some classes of bounded sets in metric spaces

Garrido, M. IsabelMeroño, Ana S.2023-06-202023-06-202012978-84-695-4421-1https://hdl.handle.net/20.500.14352/45365This 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.spaSome classes of bounded sets in metric spacesbook parthttp://cisne.sim.ucm.es/record=b3232194~S6*spirestricted access514515.1Metric-boundedTotally boundedBourbaki-boundedBourbaki-completeGeometríaTopología1204 Geometría1210 Topología