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.
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L. V. Kantorovich and G. Sh. Rubinshtein, “On a space of totally additive functions,” Vestn. Leningr. Univ., 13, No. 7, 52–59 (1958).
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).
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).
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 378, 2010, pp. 40–46.
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Zatitskiy, P.B. Canonical embeddings of compact metric spaces. J Math Sci 174, 19–22 (2011). https://doi.org/10.1007/s10958-011-0276-z
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DOI: https://doi.org/10.1007/s10958-011-0276-z