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

Elói Medina Galego. "On isomorphism classes of $C(2^{} ⊕ [0,α])$ spaces." Fundamenta Mathematicae 204.1 (2009): 87-95. <http://eudml.org/doc/282652>.

@article{ElóiMedinaGalego2009,
abstract = {We provide a complete isomorphic classification of the Banach spaces of continuous functions on the compact spaces $2^\{\} ⊕ [0,α]$, the topological sums of Cantor cubes $2^\{\}$, 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 $C(2^\{\} ⊕ [0,α])$ spaces with ≥ ℵ₀ and α ≥ ω₁ are the trivial ones. This result leads to some elementary questions on large cardinals.},
author = {Elói Medina Galego},
journal = {Fundamenta Mathematicae},
keywords = {Banach spaces of continuous functions; Cantor cube; isomorphic classification; Mazur property; sequential cardinal},
language = {eng},
number = {1},
pages = {87-95},
title = {On isomorphism classes of $C(2^\{\} ⊕ [0,α])$ spaces},
url = {http://eudml.org/doc/282652},
volume = {204},
year = {2009},
}

TY - JOUR
AU - Elói Medina Galego
TI - On isomorphism classes of $C(2^{} ⊕ [0,α])$ spaces
JO - Fundamenta Mathematicae
PY - 2009
VL - 204
IS - 1
SP - 87
EP - 95
AB - We provide a complete isomorphic classification of the Banach spaces of continuous functions on the compact spaces $2^{} ⊕ [0,α]$, the topological sums of Cantor cubes $2^{}$, 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 $C(2^{} ⊕ [0,α])$ spaces with ≥ ℵ₀ and α ≥ ω₁ are the trivial ones. This result leads to some elementary questions on large cardinals.
LA - eng
KW - Banach spaces of continuous functions; Cantor cube; isomorphic classification; Mazur property; sequential cardinal
UR - http://eudml.org/doc/282652
ER -