Journal of Mathematical Sciences

, Volume 174, Issue 1, pp 19–22 | Cite as

Canonical embeddings of compact metric spaces

  • P. B. ZatitskiyEmail author

We prove that for any infinite compact metric space, two canonical embeddings (the Hausdorff–Kuratowski and Kantorovich–Rubinshtein embeddings) do not coincide. Bibliography: 3 titles.


Russia Canonical Embedding 
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  1. 1.
    L. V. Kantorovich and G. Sh. Rubinshtein, “On a space of totally additive functions,” Vestn. Leningr. Univ., 13, No. 7, 52–59 (1958).Google Scholar
  2. 2.
    J. Melleray, F. V. Petrov, and A. M. Vershik, “Linearly rigid metric spaces and the embedding problem,” Fund, Math., 199, No. 2, 177–194 (2008).MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    P. B. Zatitskiy, “On the coincidence of the canonical embeddings of a metric space into a Banach space,” J. Math. Sci., 158, No. 6, 853–857 (2009).zbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2011

Authors and Affiliations

  1. 1.St.Petersburg State UniversitySt. PetersburgRussia

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