$C(K)$ spaces which cannot be uniformly embedded into $c_0({\mit\Gamma} )$

Tom 192 / 2006

Jan Pelant, Petr Holický, Ondřej F. K. Kalenda Fundamenta Mathematicae 192 (2006), 245-254 MSC: Primary 46B26; Secondary 54E15, 54D20. DOI: 10.4064/fm192-3-4

Streszczenie

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 $\omega _0+1$.

Autorzy

  • Jan PelantDepartment of Mathematical Analysis
    Faculty of Mathematics and Physics
    Charles University
    Sokolovská 83
    186 75 Praha 8, Czech Republic
  • Petr HolickýDepartment of Mathematical Analysis
    Faculty of Mathematics and Physics
    Charles University
    Sokolovská 83
    186 75 Praha 8, Czech Republic
    e-mail
  • Ondřej F. K. KalendaDepartment of Mathematical Analysis
    Faculty of Mathematics and Physics
    Charles University
    Sokolovská 83
    186 75 Praha 8, Czech Republic
    e-mail

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