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Finite metric spaces needing high dimension for lipschitz embeddings in banach spaces

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Abstract

We construct a sequence of metric spaces (M n) with cardM n=3n satisfying that for everyc<2, there exists a real numbera(c)>0 such that, if the Lipschitz distance fromM n to a subset of a Banach spaceE is less thanc, then dim(E) ≥a(c)n. We also prove several results about embeddings of metric spaces whose non-zero distance values are in the interval [1,2].

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Authors and Affiliations

  1. Departmento de Análisis Matemático, Universidad de Sevilla, Apdo. 1160, 41080, Sevilla, Spain

    Juan Arias-de-Reyna & Luis Rodríguez-Piazza

Authors
  1. Juan Arias-de-Reyna
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  2. Luis Rodríguez-Piazza
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Arias-de-Reyna, J., Rodríguez-Piazza, L. Finite metric spaces needing high dimension for lipschitz embeddings in banach spaces. Israel J. Math. 79, 103–111 (1992). https://doi.org/10.1007/BF02764804

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  • DOI: https://doi.org/10.1007/BF02764804

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