An Isomorphic Classification of $C({\bf 2}^{\mathfrak{m}} \times [0, \alpha])$ Spaces

Volume 57 / 2009

Elói Medina Galego Bulletin Polish Acad. Sci. Math. 57 (2009), 279-287 MSC: Primary 46B03; Secondary 03E55. DOI: 10.4064/ba57-3-9

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.

Authors

  • Elói Medina GalegoDepartment of Mathematics
    University of São Paulo
    São Paulo, Brazil 05508-090
    e-mail

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