Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Free Banach spaces and the approximation properties   We characterize the metric spaces whose free space has the bounded
approximation property through a Lipschitz analogue of the local reflexivity
principle. We show that there exist compact metric spaces whose free spaces
fail the approximation property.

32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat