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arXiv · 2201.08271

Isomorphic classification of projective tensor products of spaces of continuous functions

R. M. Causey·E. Galego·C. Samuel
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Abstract

We prove that for infinite, countable, compact, Hausdorff spaces $K,L$, $C(K)\widehat{\otimes}_\pi C(L)$ is isomorphic to exactly one of the spaces $C(\omega^{\omega^\xi})\widehat{\otimes}_\pi C(\omega^{\omega^\zeta})$, $0\leqslant \zeta\leqslant \xi<\omega_1$. We also prove that $C(K)\widehat{\otimes}_\pi C(L)$ is not isomorphic to $C(M)$ for any compact, Hausdorff space $M$.

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R. M. Causey, E. Galego, C. Samuel. 2022-01-20. Isomorphic classification of projective tensor products of spaces of continuous functions. https://arxiv.org/abs/2201.08271

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