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A Banach–Stone Theorem for Uniformly Continuous Functions

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Abstract.

 In this note we prove that the uniformity of a complete metric space X is characterized by the vector lattice structure of the set U(X) of all uniformly continuous real functions on X.

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Authors and Affiliations

  1.  Universidad de Extremadura, Badajoz, Spain, , , , , , ES

    M. Isabel Garrido

  2.  Universidad Complutense de Madrid, Spain, , , , , , ES

    Jesús A. Jaramillo

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  1. M. Isabel Garrido
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  2. Jesús A. Jaramillo
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(Received 3 March 2000; in revised form 29 June 2000)

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Garrido, M., Jaramillo, J. A Banach–Stone Theorem for Uniformly Continuous Functions. Mh Math 131, 189–192 (2000). https://doi.org/10.1007/s006050070008

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  • DOI: https://doi.org/10.1007/s006050070008

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