We provide a complete isomorphic classification of the Banach spaces of continuous functions on the compact spaces , the topological sums of Cantor cubes , with smaller than the first sequential cardinal, and intervals of ordinal numbers [0,α]. In particular, we prove that it is relatively consistent with ZFC that the only isomorphism classes of spaces with ≥ ℵ₀ and α ≥ ω₁ are the trivial ones. This result leads to some elementary questions on large cardinals.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm204-1-5,
author = {El\'oi Medina Galego},
title = {On isomorphism classes of $C(2^{} [?] [0,a])$ spaces},
journal = {Fundamenta Mathematicae},
volume = {205},
year = {2009},
pages = {87-95},
zbl = {1181.46005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm204-1-5}
}
Elói Medina Galego. On isomorphism classes of $C(2^{} ⊕ [0,α])$ spaces. Fundamenta Mathematicae, Tome 205 (2009) pp. 87-95. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm204-1-5/