Embeddings of Proper Metric Spaces into Banach Spaces
نویسنده
چکیده
We show that there exists a strong uniform embedding from any proper metric space into any Banach space without cotype. Then we prove a result concerning the Lipschitz embedding of locally finite subsets of Lp-spaces. We use this locally finite result to construct a coarse bi-Lipschitz embedding for proper subsets of any Lp-space into any Banach space X containing the l n p ’s. Finally using an argument of G. Schechtman we prove that for general proper metric spaces and for Banach spaces without cotype a converse statement holds.
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Embeddings of Locally Finite Metric Spaces into Banach Spaces
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