Geodesic
$C(K)$ spaces which cannot be uniformly embedded into $c_0({\mit\Gamma} )$
Jan Pelant1 ; Petr Holický1 ; Ondřej F. K. Kalenda1
1 Department of Mathematical Analysis Faculty of Mathematics and Physics Charles University Sokolovská 83 186 75 Praha 8, Czech Republic
Fundamenta Mathematicae, Tome 192 (2006) no. 3, pp. 245-254.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We give two examples of scattered compact spaces $K$ such that $C(K)$ is not uniformly homeomorphic to any subset of $c_0({\mit\Gamma} )$ for any set ${\mit\Gamma} $. The first one is $[0,\omega _1]$ and hence it has the smallest possible cardinality, the other one has the smallest possible height $\omega _0+1$.
DOI : 10.4064/fm192-3-4
Keywords: examples scattered compact spaces uniformly homeomorphic subset mit gamma set mit gamma first omega hence has smallest possible cardinality other has smallest possible height omega

Jan Pelant 1 ; Petr Holický 1 ; Ondřej F. K. Kalenda 1

1 Department of Mathematical Analysis Faculty of Mathematics and Physics Charles University Sokolovská 83 186 75 Praha 8, Czech Republic 
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Jan Pelant; Petr Holický; Ondřej F. K. Kalenda. $C(K)$ spaces which cannot be uniformly
 embedded into $c_0({\mit\Gamma} )$. Fundamenta Mathematicae, Tome 192 (2006) no. 3, pp. 245-254. doi : 10.4064/fm192-3-4. http://geodesic.mathdoc.fr/articles/10.4064/fm192-3-4/

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