Covering an uncountable square by countable many continuous functions

Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F12%3A00387008" target="_blank" >RIV/67985840:_____/12:00387008 - isvavai.cz</a>
Výsledek na webu
<a href="http://dx.doi.org/10.1090/S0002-9939-2012-11292-4" target="_blank" >http://dx.doi.org/10.1090/S0002-9939-2012-11292-4</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 countable 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 X X, where X is uncountable. This extends Sierpiński's theorem from 1919, saying that S S can be covered by countably many graphs of functions and inverses of functions if and only if |S| <= ? 1. Using forcing and absoluteness arguments, we also prove the existence of countably many 1-Lipschitz functions on the Cantor set endowed withthe standard non-archimedean metric that cover an uncountable square.
Název v anglickém jazyce
Covering an uncountable square by countable 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 X X, where X is uncountable. This extends Sierpiński's theorem from 1919, saying that S S can be covered by countably many graphs of functions and inverses of functions if and only if |S| <= ? 1. Using forcing and absoluteness arguments, we also prove the existence of countably many 1-Lipschitz functions on the Cantor set endowed withthe 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>Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění
2012
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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