2026-06-29T07:49:20Zhttps://docta.ucm.es/rest/oai/requestoai:docta.ucm.es:20.500.14352/453652025-12-10T11:04:31Zcom_20.500.14352_14col_20.500.14352_21
Some classes of bounded sets in metric spaces
Garrido Carballo, María Isabel
Meroño Moreno, Ana Soledad
514
515.1
Metric-bounded
Totally bounded
Bourbaki-bounded
Bourbaki-complete
Geometría
Topología
1204 Geometría
1210 Topología
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.
Ministerio de Ciencia, Innovación y Universidades (España)
Fundación Caja-Madrid
Universidad Complutense de Madrid
Depto. de Álgebra, Geometría y Topología
Fac. de Ciencias Matemáticas
Instituto de Matemática Interdisciplinar (IMI)
TRUE
pub
2023-06-20T05:44:33Z
2023-06-20T05:44:33Z
2012
book part
https://hdl.handle.net/20.500.14352/45365
XXXX-XXXX
eng
info:eu-repo/grantAgreement/MICINN//MTM2009-07848/ES/Analisis Funcional No-Lineal Y Geometrico/
open access
application/pdf
UCM