Abstract
We prove that if K and L are compact spaces and C(K) and C(L) are isomorphic as Banach spaces, then K has a π-base consisting of open sets U such that Ū is a continuous image of some compact subspace of L. This sheds new light on isomorphic classes of spaces of the form \(C({[0,1]^\kappa })\) and spaces C(K) where K is Corson compact.
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The research was partially supported by MNiSW Grant N N201 418939 (2010–2013). The author would like to thank Eloi Medina Galego, Mikołaj Krupski and Witold Marciszewski for correspondence concerning the subject. He is grateful to the referee for a very careful reading and suggesting several improvements.
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Plebanek, G. On isomorphisms of Banach spaces of continuous functions. Isr. J. Math. 209, 1–13 (2015). https://doi.org/10.1007/s11856-015-1210-8
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DOI: https://doi.org/10.1007/s11856-015-1210-8