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Two classes of metric spaces Garrido Carballo, María Isabel Meroño Moreno, Ana Soledad 514 Metric spaces real-valued uniformly continuous functions realvalued Lipschitz functions bornologies Bourbaki-boundedness countable uniform partitions small-determined spaces B-simple spaces. Topología 1210 Topología The class of metric spaces (X,d) known as small-determined spaces, introduced by Garrido and Jaramillo, are properly defined by means of some type of real-valued Lipschitz functions on X. On the other hand, B-simple metric spaces introduced by Hejcman are defined in terms of some kind of bornologies of bounded subsets of X. In this note we present a common framework where both classes of metric spaces can be studied which allows us to see not only the relationships between them but also to obtain new internal characterizations of these metric properties. Ministerio de Economía y Competitividad (España) Depto. de Álgebra, Geometría y Topología Fac. de Ciencias Matemáticas TRUE pub 2023-06-18T06:53:21Z 2023-06-18T06:53:21Z 2016 journal article https://hdl.handle.net/20.500.14352/24504 1576-9402 10.4995/agt.2016.4401 eng info:eu-repo/grantAgreement/MINECO//MTM2012-34341/ES/ Garrido, Isabel, y Ana S. Meroño. «Two classes of metric spaces». Applied General Topology, vol. 17, n.o 1, abril de 2016, p. 57. DOI.org (Crossref), https://doi.org/10.4995/agt.2016.4401. Atribución-NoComercial-SinDerivadas 3.0 España https://creativecommons.org/licenses/by-nc-nd/3.0/es/ open access application/pdf Universidad Politécnica de Valencia