Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On embeddings of finite subsets of $\ell_2$   We study finite subsets of $\ell_2$, and more generally any metric space, and
consider whether these isometrically embed into a Banach space. Our results
partially answer a question of Ostrovskii, on whether every
infinite-dimensional Banach space contains every finite subset of $\ell_2$
isometrically.
  The updated version contains acknowledgement that Theorem 3.1 has been proven
previously in a paper of Shkarin.

10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex