Geodesic
Lipschitz-quotients and the Kunen-Martin Theorem
Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) no. 4, pp. 641-648.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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 
@article{CMUC_2001__42_4_a4,
     author = {Dutrieux, Yves},
     title = {Lipschitz-quotients and the {Kunen-Martin} {Theorem}},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {641--648},
     publisher = {mathdoc},
     volume = {42},
     number = {4},
     year = {2001},
     mrnumber = {1883373},
     zbl = {1069.03035},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2001__42_4_a4/}
}
TY  - JOUR
AU  - Dutrieux, Yves
TI  - Lipschitz-quotients and the Kunen-Martin Theorem
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 2001
SP  - 641
EP  - 648
VL  - 42
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMUC_2001__42_4_a4/
LA  - en
ID  - CMUC_2001__42_4_a4
ER  - 
%0 Journal Article
%A Dutrieux, Yves
%T Lipschitz-quotients and the Kunen-Martin Theorem
%J Commentationes Mathematicae Universitatis Carolinae
%D 2001
%P 641-648
%V 42
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMUC_2001__42_4_a4/
%G en
%F CMUC_2001__42_4_a4
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/