Abstract
We give a purely metric proof of the following result: let (X,d) be a separable metric space; for all ɛ>0 there is an injectionf ofX inC +0 such that:
It is a more precise version of a result of I. Aharoni. We extend it to metric space of cardinal α+ (for infinite α).
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References
I. Aharoni,Every separable metric space is Lipschitz equivalent to a subset of c +0 , Israel J. Math.19 (1974), 284–291.
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Assouad, P. Remarques sur un article de Israel Aharoni sur les prolongements lipschitziens dansc 0 . Israel J. Math. 31, 97–100 (1978). https://doi.org/10.1007/BF02761384
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DOI: https://doi.org/10.1007/BF02761384