| Title:
|
$\sigma $-porosity is separably determined (English) |
| Author:
|
Cúth, Marek |
| Author:
|
Rmoutil, Martin |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
63 |
| Issue:
|
1 |
| Year:
|
2013 |
| Pages:
|
219-234 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove a separable reduction theorem for $\sigma $-porosity of Suslin sets. In particular, if $A$ is a Suslin subset in a Banach space $X$, then each separable subspace of $X$ can be enlarged to a separable subspace $V$ such that $A$ is $\sigma $-porous in $X$ if and only if $A\cap V$ is $\sigma $-porous in $V$. Such a result is proved for several types of $\sigma $-porosity. The proof is done using the method of elementary submodels, hence the results can be combined with other separable reduction theorems. As an application we extend a theorem of L. Zajíček on differentiability of Lipschitz functions on separable Asplund spaces to the nonseparable setting. (English) |
| Keyword:
|
elementary submodel |
| Keyword:
|
separable reduction |
| Keyword:
|
porous set |
| Keyword:
|
$\sigma $-porous set |
| MSC:
|
03C15 |
| MSC:
|
28A05 |
| MSC:
|
49J50 |
| MSC:
|
54E35 |
| MSC:
|
54E52 |
| MSC:
|
54H05 |
| MSC:
|
58C20 |
| idZBL:
|
Zbl 1274.54093 |
| idMR:
|
MR3035508 |
| DOI:
|
10.1007/s10587-013-0015-3 |
| . |
| Date available:
|
2013-03-01T16:17:53Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143181 |
| . |
| 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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| 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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| 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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| . |
