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Israel Journal of Mathematics

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

On isomorphisms of Banach spaces of continuous functions

  • Grzegorz PlebanekEmail author
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.

Keywords

Banach Space Compact Space Continuous Image Nonempty Open Subset Isomorphic Embedding 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Hebrew University of Jerusalem 2015

Authors and Affiliations

  1. 1.Instytut MatematycznyUniwersytet WrocławskiWrocławPoland

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