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Embedding metric spaces in Euclidean space

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Abstract

In this paper, we give necessary and sufficient conditions for embedding a given metric space in Euclidean space. We shall introduce the notions of flatness and dimension for metric spaces and prove that a metric space can be embedded in Euclidean n-space if and only if the metric space is flat and of dimension less than or equal to n.

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References

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Authors and Affiliations

  1. Department of Mathematics, California State University, 94542, Hayward, California, USA

    C. L. Morgan

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  1. C. L. Morgan
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Morgan, C.L. Embedding metric spaces in Euclidean space. J Geom 5, 101–107 (1974). https://doi.org/10.1007/BF01954540

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  • DOI: https://doi.org/10.1007/BF01954540

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