About: Covering an uncountable square by countably many continuous functions

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An Entity of Type : http://linked.opendata.cz/ontology/domain/vavai/Vysledek, within Data Space : linked.opendata.cz associated with source document(s)

Attributes	Values
rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
rdfs:seeAlso	http://www.ams.org/journals/proc/2012-140-12/S0002-9939-2012-11292-4/home.html
Description	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 $X\times X$, where $X\subs\Err$ is uncountable. This extends Sierpiński''s theorem from 1919, saying that $S\times S$ can be covered by countably many graphs of functions and inverses of functions if and only if $\|S\|\loe\aleph_1$. 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. 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 $X\times X$, where $X\subs\Err$ is uncountable. This extends Sierpiński''s theorem from 1919, saying that $S\times S$ can be covered by countably many graphs of functions and inverses of functions if and only if $\|S\|\loe\aleph_1$. 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. (en)
Title	Covering an uncountable square by countably many continuous functions Covering an uncountable square by countably many continuous functions (en)
skos:prefLabel	Covering an uncountable square by countably many continuous functions Covering an uncountable square by countably many continuous functions (en)
skos:notation	RIV/00216208:11320/12:10103608!RIV13-AV0-11320___
http://linked.open...avai/riv/aktivita	P S Z
http://linked.open...avai/riv/aktivity	P(IAA100190901), S, Z(AV0Z10190503)
http://linked.open...iv/cisloPeriodika	5
http://linked.open...vai/riv/dodaniDat	2013
http://linked.open...aciTvurceVysledku	Vejnar, Benjamin
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Univerzita Karlova v Praze / Matematicko-fyzikální fakulta
http://linked.open...dnocenehoVysledku	128953
http://linked.open...ai/riv/idVysledku	RIV/00216208:11320/12:10103608
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	set of cardinality $\aleph_1$; covering by continuous functions; Uncountable square (en)
http://linked.open.../riv/klicoveSlovo	Uncountable square covering by continuous functions set of cardinality $\aleph_1$
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[C97C3A04C7DC]
http://linked.open...i/riv/nazevZdroje	Proceedings of the American Mathematical Society
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	Topological and geometric structures in Banach spaces
http://linked.open...UplatneniVysledku	2012
http://linked.open...v/svazekPeriodika	140
http://linked.open...iv/tvurceVysledku	Kubiś, Wieslaw Vejnar, Benjamin
http://linked.open...ain/vavai/riv/wos	000312117500033
http://linked.open...n/vavai/riv/zamer	Rozvoj a prohloubení obecných matematických poznatků a jejich užití v dalších vědních oborech a v praxi
issn	0002-9939
number of pages	10 (xsd:int)
http://bibframe.org/vocab/doi	10.1090/S0002-9939-2012-11292-4
http://localhost/t...ganizacniJednotka	11320

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