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Embedding metric spaces in Euclidean space (1974)

Morgan, C. L.

Springer

Journal of geometry 5 (1974), S. 101-107

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ISSN: 1420-8997

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: 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.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01954540

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