Abstract
Galego and Samuel showed that if K, L are metrizable, compact, Hausdorff spaces, then
$C(K)\widehat{\otimes}_\pi C(L)$
is c0-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 twofold projective tensor product to the general n-fold projective tensor product to show that for any
$n\in\mathbb{N}$
and compact, Hausdorff spaces K1, …, K
n
,
$\widehat{\otimes}_{\pi, i=1}^n C(K_i)$
is c0-saturated if and only if it is subprojective if and only if each K
i
is scattered.
Tropical ideals do not realise all Bergman fans
