Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lipschitz Embeddings of Metric Spaces into $c_0$   Let $M$ be a separable metric space. We say that $f=(f_n):M\to c_0$ is a
good-$\lambda$-embedding if, whenever $x,y\in M$, $x\ne y$ implies
$d(x,y)\le\Vert f(x)-f(y)\Vert$ and, for each $n$, $Lip(f_n)<\lambda$, where
$Lip(f_n)$ denotes the Lipschitz constant of $f_n$. We prove that there exists
a good-$\lambda$-embedding from $M$ into $c_0$ if and only if $M$ satisfies an
internal property called $\pi(\lambda)$. As a consequence, we obtain that for
any separable metric space $M$, there exists a good-$2$-embedding from $M$ into
$c_0$. These statements slightly extend former results obtained by N. Kalton
and G. Lancien, with simplified proofs.

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The categories of this paper are: nlin
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The categories of this paper are: funct-an
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The categories of this paper are: q-bio
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The categories of this paper are: astro-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: econ
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The categories of this paper are: stat
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: cs
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The categories of this paper are: physics
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The categories of this paper are: hep-ph