On isomorphism classes of $C({\bf 2}^{\mathfrak{m}} \oplus [0, \alpha])$ spaces

Elói Medina Galego¹

¹ Department of Mathematics University of São Paulo São Paulo, Brazil 05508-090

Fundamenta Mathematicae, Tome 204 (2009) no. 1, pp. 87-95

Résumé

We provide a complete isomorphic classification of the Banach spaces of continuous functions on the compact spaces ${\bf 2}^{\mathfrak{m}} \oplus [0, \alpha]$, the topological sums of Cantor cubes ${\bf 2}^{\mathfrak{m}}$, with $\mathfrak{m}$ smaller than the first sequential cardinal, and intervals of ordinal numbers $[0, \alpha]$. In particular, we prove that it is relatively consistent with ZFC that the only isomorphism classes of $C({\bf 2}^{\mathfrak{m}} \oplus [0, \alpha])$ spaces with $\mathfrak{m} \geq \aleph_{0}$ and $\alpha \geq \omega_1$ are the trivial ones. This result leads to some elementary questions on large cardinals.

Détail

DOI : 10.4064/fm204-1-5

Mots-clés : provide complete isomorphic classification banach spaces continuous functions compact spaces mathfrak oplus alpha topological sums cantor cubes mathfrak mathfrak smaller first sequential cardinal intervals ordinal numbers alpha particular prove relatively consistent zfc only isomorphism classes mathfrak oplus alpha spaces mathfrak geq aleph alpha geq omega trivial result leads elementary questions large cardinals