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On the inverse of Mañé's projection


Author: H. Movahedi-Lankarani
Journal: Proc. Amer. Math. Soc. 116 (1992), 555-560
MSC: Primary 54E35; Secondary 46S10, 54C25
DOI: https://doi.org/10.1090/S0002-9939-1992-1111436-3
MathSciNet review: 1111436
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Abstract: We show that every compact ultrametric space is bi-Lipschitz embeddable in a Hilbert space. We also provide an example of a compact ultrametric space whose fractal (and hence Hausdorff) dimension is finite, but which cannot be bi-Lipschitz embedded in any finite dimensional Euclidean space. This example, in particular, establishes that the inverse of Mañé's projection need not be Lipschitz even in the case of finite fractal dimension.


References [Enhancements On Off] (What's this?)

  • [1] Patrice Assouad, Plongements lipschitziens dans 𝑅ⁿ, Bull. Soc. Math. France 111 (1983), no. 4, 429–448 (French, with English summary). MR 763553
  • [2] Alp Eden, Ciprian Foias, Basil Nicolaenko, and Roger Temam, Ensembles inertiels pour des équations d’évolution dissipatives, C. R. Acad. Sci. Paris Sér. I Math. 310 (1990), no. 7, 559–562 (French, with English summary). MR 1050131
  • [3] R. Mañé, Lecture Notes in Math., vol. 898, Springer-Verlag, New York, 1981, pp. 230-242.
  • [4] H. Movahedi-Lankarani, Minimal Lipschitz embeddings, Ph.D. Thesis, Pennsylvania State Univ., 1990.

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DOI: https://doi.org/10.1090/S0002-9939-1992-1111436-3
Article copyright: © Copyright 1992 American Mathematical Society