Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Subprojectivity of projective tensor products of Banach spaces of
  continuous functions   Galego and Samuel showed that if $K,L$ are metrizable, compact, Hausdorff
spaces, then $C(K)\widehat{\otimes}_\pi C(L)$ is $c_0$-saturated if and only if
it is subprojective if and only if $K$ and $L$ are both scattered. We remove
the hypothesis of metrizability from their result, and extend it from the case
of the two-fold projective tensor product to the general $n$-fold projective
tensor product to show that for any $n\in\mathbb{N}$ and compact, Hausdorff
spaces $K_1, \ldots, K_n$, $\widehat{\otimes}_{\pi, i=1}^n C(K_i)$ is
$c_0$-saturated if and only if it is subprojective if and only if each $K_i$ is
scattered.

1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat