An Isomorphic Classification of $C\left(2^{}\times [0,\alpha ]\right)$ Spaces

Elói Medina Galego. "An Isomorphic Classification of $C(2^{} × [0,α])$ Spaces." Bulletin of the Polish Academy of Sciences. Mathematics 57.3 (2009): 279-287. <http://eudml.org/doc/281260>.

@article{ElóiMedinaGalego2009,
abstract = {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 $C(2^\{\} × [0,α])$ of all real continuous functions defined on the compact spaces $2^\{\} × [0,α]$, the topological product of the Cantor cubes $2^\{\}$ 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 $C(2^\{\} × [0,α])$ spaces.},
author = {Elói Medina Galego},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {Banach spaces of continuous functions; Cantor cube; isomorphic classification; Mazur property; sequential cardinal},
language = {eng},
number = {3},
pages = {279-287},
title = {An Isomorphic Classification of $C(2^\{\} × [0,α])$ Spaces},
url = {http://eudml.org/doc/281260},
volume = {57},
year = {2009},
}

TY - JOUR
AU - Elói Medina Galego
TI - An Isomorphic Classification of $C(2^{} × [0,α])$ Spaces
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2009
VL - 57
IS - 3
SP - 279
EP - 287
AB - 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 $C(2^{} × [0,α])$ of all real continuous functions defined on the compact spaces $2^{} × [0,α]$, the topological product of the Cantor cubes $2^{}$ 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 $C(2^{} × [0,α])$ spaces.
LA - eng
KW - Banach spaces of continuous functions; Cantor cube; isomorphic classification; Mazur property; sequential cardinal
UR - http://eudml.org/doc/281260
ER -