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 of all real continuous functions defined on the compact spaces , the topological product of the Cantor cubes with 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 spaces.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba57-3-9,
author = {El\'oi Medina Galego},
title = {An Isomorphic Classification of $C(2^{} $\times$ [0,$\alpha$])$ Spaces},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {57},
year = {2009},
pages = {279-287},
zbl = {1195.46009},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba57-3-9}
}
Elói Medina Galego. An Isomorphic Classification of $C(2^{} × [0,α])$ Spaces. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 57 (2009) pp. 279-287. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba57-3-9/