Separable reduction theorems by the method of elementary submodels

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F12%3A10129155" target="_blank" >RIV/00216208:11320/12:10129155 - isvavai.cz</a>
Result on the web
<a href="http://journals.impan.gov.pl/fm/" target="_blank" >http://journals.impan.gov.pl/fm/</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4064/fm219-3-1" target="_blank" >10.4064/fm219-3-1</a>

Result language
angličtina
Original language name
Separable reduction theorems by the method of elementary submodels
Original language description
We simplify the presentation of the method of elementary submodels and we show that it can be used for simplifying proofs of existing separable reduction theorems and for obtaining new ones. Given a nonseparable Banach space $X$ and either a subset $Asubset X$ or a function $f$ defined on $X$, we are able for certain properties produce a separable subspace of $X$ which determines whether $A$ or $f$ has the property. Such results are proved for properties of sets ''to be dense, nowhere dense, meager, residual or porous'' and for properties of functions ''to be continuous, semicontinuous or Fr'echet differentiable''. Our method of creating separable subspaces enables us to combine our results, so we easily get separable reductions of properties such as''to be continuous on a dense subset'', ''to be Fr'echet differentiable on a residual subset'', etc. Finally, we show some applications of presented separable reduction theorems and demonstrate that some results of Zaj'{i}v{c}ek, Lin
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
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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