Separable reduction theorems by the method of elementary submodels

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Separable reduction theorems by the method of elementary submodels

Popis výsledku v původním jazyce

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

Název v anglickém jazyce

Separable reduction theorems by the method of elementary submodels

Popis výsledku anglicky

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

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

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Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2012

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Fundamenta Mathematicae

ISSN

0016-2736

e-ISSN

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Svazek periodika

2012

Číslo periodika v rámci svazku

219

Stát vydavatele periodika

PL - Polská republika

Počet stran výsledku

32

Strana od-do

191-222

Kód UT WoS článku

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EID výsledku v databázi Scopus

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