Two classes of metric spaces

Authors

  • Isabel Garrido Universidad Complutense de Madrid
  • Ana S. Meroño Universidad Complutense de Madrid

DOI:

https://doi.org/10.4995/agt.2016.4401

Keywords:

metric spaces, real-valued uniformly continuous functions, real-valued Lipschitz functions, bornologies, Bourbaki-boundedness, countable uniform partitions, small-determined spaces, B-simple spaces.

Abstract

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.

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References

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(http://dx.doi.org/10.2140/pjm.1958.8.11)

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(http://dx.doi.org/10.1016/j.jmaa.2007.08.028)

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M. I. Garrido and A. S. Meroño, The Samuel realcompactification of a metric space, submitted.

J. Hejcman, Boundedness in uniform spaces and topological groups, Czechoslovak Math. J. 9 (1959), 544-563.

(http://dx.doi.org/10.1007/BF01556943)

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(http://dx.doi.org/10.1016/0166-8641(86)90006-4)

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Published

2016-04-12

How to Cite

[1]
I. Garrido and A. S. Meroño, “Two classes of metric spaces”, Appl. Gen. Topol., vol. 17, no. 1, pp. 57–70, Apr. 2016.

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Articles