An Isomorphic Classification of C(2m x [0, a]) Spaces

摘要

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