| Title:
|
Lipschitz-quotients and the Kunen-Martin Theorem (English) |
| Author:
|
Dutrieux, Yves |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
42 |
| Issue:
|
4 |
| Year:
|
2001 |
| Pages:
|
641-648 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Lipschitz equivalences |
| Keyword:
|
Szenk index |
| MSC:
|
03E15 |
| MSC:
|
46B20 |
| idZBL:
|
Zbl 1069.03035 |
| idMR:
|
MR1883373 |
| . |
| Date available:
|
2009-01-08T19:17:14Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119280 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| . |
