Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On relations between transportation cost spaces and $\ell_1$   The present paper deals with some structural properties of transportation
cost spaces, also known as Arens-Eells spaces, Lipschitz-free spaces and
Wasserstein spaces. The main results of this work are: (1) A necessary and
sufficient condition on an infinite metric space $M$, under which the
transportation cost space on $M$ contains an isometric copy of $\ell_1$. The
obtained condition is applied to answer the open questions asked by C\'uth and
Johanis (2017) concerning several specific metric spaces. (2) The description
of the transportation cost space of a weighted finite graph $G$ as the quotient
$\ell_1(E(G))/Z(G)$, where $E(G)$ is the edge set and $Z(G)$ is the cycle space
of $G$. This is a generalization of the previously known result to the case of
any finite metric space.

4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio