Covering an uncountable square by countably many continuous functions

Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F12%3A10103608" target="_blank" >RIV/00216208:11320/12:10103608 - isvavai.cz</a>
Výsledek na webu
<a href="http://www.ams.org/journals/proc/2012-140-12/S0002-9939-2012-11292-4/home.html" target="_blank" >http://www.ams.org/journals/proc/2012-140-12/S0002-9939-2012-11292-4/home.html</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1090/S0002-9939-2012-11292-4" target="_blank" >10.1090/S0002-9939-2012-11292-4</a>

Jazyk výsledku
angličtina
Název v původním jazyce
Covering an uncountable square by countably many continuous functions
Popis výsledku v původním jazyce
We prove that there exists a countable family of continuous real functions whose graphs together with their inverses cover an uncountable square, i.e. a set of the form $Xtimes X$, where $XsubsErr$ is uncountable. This extends Sierpiński''s theorem from 1919, saying that $Stimes S$ can be covered by countably many graphs of functions and inverses of functions if and only if $|S|loealeph_1$. Using forcing and absoluteness arguments, we also prove the existence of countably many $1$-Lipschitz functions on the Cantor set endowed with the standard non-archimedean metric that cover an uncountable square.
Název v anglickém jazyce
Covering an uncountable square by countably many continuous functions
Popis výsledku anglicky
We prove that there exists a countable family of continuous real functions whose graphs together with their inverses cover an uncountable square, i.e. a set of the form $Xtimes X$, where $XsubsErr$ is uncountable. This extends Sierpiński''s theorem from 1919, saying that $Stimes S$ can be covered by countably many graphs of functions and inverses of functions if and only if $|S|loealeph_1$. Using forcing and absoluteness arguments, we also prove the existence of countably many $1$-Lipschitz functions on the Cantor set endowed with the standard non-archimedean metric that cover an uncountable square.

Druh
J<sub>x</sub> - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
CEP obor
BA - Obecná matematika
OECD FORD obor
—

Projekt
<a href="/cs/project/IAA100190901" target="_blank" >IAA100190901: Topologické a geometrické struktury v Banachovych prostorech</a><br>
Návaznosti
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>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

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