Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Coarse embeddings into $c_0(\Gamma)$   Let $\lambda$ be a large enough cardinal number (assuming GCH it suffices to
let $\lambda=\aleph_\omega$). If $X$ is a Banach space with
$\text{dens}(X)\ge\lambda$, which admits a coarse (or uniform) embedding into
any $c_0(\Gamma)$, then $X$ fails to have nontrivial cotype, i.e. $X$ contains
$\ell_\infty^n$ $C$-uniformly for every $C>1$. In the special case when $X$ has
a symmetric basis, we may even conclude that it is linearly isomorphic with
$c_0(\text{dens}X)$.

12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas