Geodesic
Lipschitz-quotients and the Kunen-Martin Theorem
Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) no. 4, pp. 641-648
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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.
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.
Classification : 03E15, 46B20
Keywords: Lipschitz equivalences; Szenk index 
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     author = {Dutrieux, Yves},
     title = {Lipschitz-quotients and the {Kunen-Martin} {Theorem}},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {641--648},
     year = {2001},
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Dutrieux, Yves. Lipschitz-quotients and the Kunen-Martin Theorem. Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) no. 4, pp. 641-648. http://geodesic.mathdoc.fr/item/CMUC_2001_42_4_a4/