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An isomorphic classification of C(2m x [0, α]) spaces

Galego E. M.

Bulletin of the Polish Academy of Sciences. Mathematics

2009

Vol. 57, no 3-4

279-287

We present an extension of the classical isomorphic classification of the Banach spaces C([0, α]) of all real continuous functions defined on the nondenumerable intervals of ordinals [0, α]. As an application, we establish the isomorphic classification of the Banach spaces C(2m x [0, α]) of all real continuous functions defined on the compact spaces 2m x [0, α], the topological product of the Cantor cubes 2m with m smaller than the first sequential cardinal, and intervals of ordinal numbers [0, α]. Consequently, it is relatively consistent with ZFC that this yields a complete isomorphic classification of C(2m x [0, α]) spaces.