Israel Journal of Mathematics

, Volume 209, Issue 1, pp 1–13 | Cite as

On isomorphisms of Banach spaces of continuous functions

Article

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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© Hebrew University of Jerusalem 2015

Authors and Affiliations

  1. 1.Instytut MatematycznyUniwersytet WrocławskiWrocławPoland

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