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 particular the case when two Banach spaces are Lipschitz-homeomorphic. This provides information on the Cantor index of scattered compact sets $K$ and $L$ such that $C(L)$ is a Lipschitz-quotient of $C(K)$ (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