Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Supports and extreme points in Lipschitz-free spaces   For a complete metric space $M$, we prove that the finitely supported extreme
points of the unit ball of the Lipschitz-free space $\mathcal{F}(M)$ are
precisely the elementary molecules $(\delta(p)-\delta(q))/d(p,q)$ defined by
pairs of points $p,q$ in $M$ such that the triangle inequality
$d(p,q)<d(p,r)+d(q,r)$ is strict for any $r\in M$ different from $p$ and $q$.
To this end, we show that the class of Lipschitz-free spaces over closed
subsets of $M$ is closed under arbitrary intersections when $M$ has finite
diameter, and that this allows a natural definition of the support of elements
of $\mathcal{F}(M)$.

3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph