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Yves Dutrieux EFI?DEJGKJEAJI =@ JDA KA=HJE 6DAHA

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Yves Dutrieux

Lipschitz-quotients and the Kunen-Martin Theorem

Comment.Math.Univ.Carolinae 42,4 (2001) 641-648.

Abstract: We show that there is a universal control on the Szlenk index of a Lipschitz-quotient of a Banach space with countable Szlenk index. It is in partic- ular the case when two Banach spaces are Lipschitz-homeomorphic. This provides information on the Cantor index of scattered compact setsKandLsuch thatC(L) is a Lipschitz-quotient ofC(K) (that is the case in particular when these two spaces are Lipschitz-homeomorphic). The proof requires tools of descriptive set theory.

Keywords: Lipschitz equivalences, Szenk index AMS Subject Classification: 03E15, 46B20

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