An Isomorphic Classification of $C({\bf 2}^{\mathfrak{m}} \times [0, \alpha])$ Spaces
Volume 57 / 2009
Abstract
\def\mathfrak#1{{\mathfrak#1}}We present an extension of the classical isomorphic classification of the Banach spaces $C([0, \alpha])$ of all real continuous functions defined on the nondenumerable intervals of ordinals $[0, \alpha]$. As an application, we establish the isomorphic classification of the Banach spaces $C({\bf 2}^{\mathfrak{m}} \times [0, \alpha])$ of all real continuous functions defined on the compact spaces ${\bf 2}^{\mathfrak{m}} \times [0, \alpha]$, the topological product of the Cantor cubes ${\bf 2}^{\mathfrak{m}}$ with $\mathfrak{m}$ smaller than the first sequential cardinal, and intervals of ordinal numbers $[0, \alpha]$. Consequently, it is relatively consistent with ZFC that this yields a complete isomorphic classification of $C({\bf 2}^{\mathfrak{m}} \times [0, \alpha])$ spaces.
