?-porosity is separably determined

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F13%3A10159050" target="_blank" >RIV/00216208:11320/13:10159050 - isvavai.cz</a>
Result on the web
<a href="http://link.springer.com/article/10.1007%2Fs10587-013-0015-3" target="_blank" >http://link.springer.com/article/10.1007%2Fs10587-013-0015-3</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10587-013-0015-3" target="_blank" >10.1007/s10587-013-0015-3</a>

Result language
angličtina
Original language name
?-porosity is separably determined
Original language description
We prove a separable reduction theorem for ?-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 ?-porous in X if and only if $Acap V$ is ?-porous in V . Such a result is proved for several types of ?-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 theoremof L. Zajíček on differentiability of Lipschitz functions on separable Asplund spaces to the nonseparable setting.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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