On isomorphism classes of $C(2^{𝔪} ⊕ [0,α])$ spaces

• Autorzy: Elói Medina Galego
• Języki publikacji: EN

Abstrakty

EN

We provide a complete isomorphic classification of the Banach spaces of continuous functions on the compact spaces $2^{𝔪} ⊕ [0,α]$, the topological sums of Cantor cubes $2^{𝔪}$, with 𝔪 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 $C(2^{𝔪} ⊕ [0,α])$ spaces with 𝔪 ≥ ℵ₀ and α ≥ ω₁ are the trivial ones. This result leads to some elementary questions on large cardinals.

Kategorie tematyczne

• 46E15: Banach spaces of continuous, differentiable or analytic functions
• 03E55: Large cardinals
• 46B03: Isomorphic theory (including renorming) of Banach spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2009
• Tom: 204
• Numer: 1
• Strony: 87-95

Daty

wydano

2009

Twórcy

autor

Elói Medina Galego

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

Identyfikatory

DOI

10.4064/fm204-1-5