About: $F\sb \sigma$-additive families and the invariance of Borel classes

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	We prove that any $F_\sigma$-additive family $\A$ of sets in an absolutely Souslin metric space has a $\sigma$-discrete refinement provided every partial selector set for $\A$ is $\sigma$-discrete. As a corollary we obtain that every mapping of a metric space onto an absolutely Souslin metric space, which maps $F_\sigma$-sets to $F_\sigma$-sets and has complete fibers, admits a section of the first class. The invariance of Borel and Souslin sets under mappings with complete fibers, which preserves $F_\sigma$-sets, is shown as an application of the previous result. We prove that any $F_\sigma$-additive family $\A$ of sets in an absolutely Souslin metric space has a $\sigma$-discrete refinement provided every partial selector set for $\A$ is $\sigma$-discrete. As a corollary we obtain that every mapping of a metric space onto an absolutely Souslin metric space, which maps $F_\sigma$-sets to $F_\sigma$-sets and has complete fibers, admits a section of the first class. The invariance of Borel and Souslin sets under mappings with complete fibers, which preserves $F_\sigma$-sets, is shown as an application of the previous result. (en) Je ukázáno, že $F$-sigma aditivní systém množin v úplném metrickém prostoru má $\sigma$-diskrétní zjemnění. (cs)
Title	$F\sb \sigma$-additive families and the invariance of Borel classes $F$-sigma aditivní systémy množin a invariance borelovských tříd (cs) $F\sb \sigma$-additive families and the invariance of Borel classes (en)
skos:prefLabel	$F\sb \sigma$-additive families and the invariance of Borel classes $F$-sigma aditivní systémy množin a invariance borelovských tříd (cs) $F\sb \sigma$-additive families and the invariance of Borel classes (en)
skos:notation	RIV/00216208:11320/05:00001384!RIV06-MSM-11320___
http://linked.open.../vavai/riv/strany	905;915
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(GA201/03/0935), P(GP201/03/D120), Z(MSM 113200007)
http://linked.open...iv/cisloPeriodika	3
http://linked.open...vai/riv/dodaniDat	2006
http://linked.open...aciTvurceVysledku	Spurný, Jiří
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	522193
http://linked.open...ai/riv/idVysledku	RIV/00216208:11320/05:00001384
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	$F\sb; \sigma$-additive; families; invariance; Borel; classes (en)
http://linked.open.../riv/klicoveSlovo	families classes invariance $F\sb \sigma$-additive Borel
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[191D553B8861]
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	1 (xsd:int)
http://linked.open...vavai/riv/projekt	Functional and Analytical Methods of Modern Analysis Descriptive properties of sets and functions in the Choquet theory of function spaces
http://linked.open...UplatneniVysledku	2005
http://linked.open...v/svazekPeriodika	133
http://linked.open...iv/tvurceVysledku	Spurný, Jiří
http://linked.open...n/vavai/riv/zamer	http://linked.opendata.cz/resource/domain/vavai/zamer/MSM%20113200007
issn	0002-9939
number of pages	11 (xsd:int)
http://localhost/t...ganizacniJednotka	11320

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