Geodesic
SUBPROJECTIVITY OF PROJECTIVE TENSOR PRODUCTS OF BANACH SPACES OF CONTINUOUS FUNCTIONS
Glasgow mathematical journal, Tome 64 (2022) no. 2, pp. 292-305

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DOI

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, ..., Kn, $\widehat{\otimes}_{\pi, i=1}^n C(K_i)$ is c0-saturated if and only if it is subprojective if and only if each Ki is scattered. 
CAUSEY, R.M. SUBPROJECTIVITY OF PROJECTIVE TENSOR PRODUCTS OF BANACH SPACES OF CONTINUOUS FUNCTIONS. Glasgow mathematical journal, Tome 64 (2022) no. 2, pp. 292-305. doi: 10.1017/S0017089521000100
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     title = {SUBPROJECTIVITY {OF} {PROJECTIVE} {TENSOR} {PRODUCTS} {OF} {BANACH} {SPACES} {OF} {CONTINUOUS} {FUNCTIONS}},
     journal = {Glasgow mathematical journal},
     pages = {292--305},
     year = {2022},
     volume = {64},
     number = {2},
     doi = {10.1017/S0017089521000100},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089521000100/}
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