$C(K)$ spaces which cannot be uniformly embedded into $c_0({\mit\Gamma} )$
Volume 192 / 2006
Fundamenta Mathematicae 192 (2006), 245-254
MSC: Primary 46B26; Secondary 54E15, 54D20.
DOI: 10.4064/fm192-3-4
Abstract
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 $\omega _0+1$.
