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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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