This HTML5 document contains 47 embedded RDF statements represented using HTML+Microdata notation.

The embedded RDF content will be recognized by any processor of HTML5 Microdata.

Namespace Prefixes

PrefixIRI
dctermshttp://purl.org/dc/terms/
n17http://localhost/temp/predkladatel/
n7http://linked.opendata.cz/resource/domain/vavai/projekt/
n6http://linked.opendata.cz/resource/domain/vavai/riv/tvurce/
n18http://linked.opendata.cz/ontology/domain/vavai/
n11http://linked.opendata.cz/resource/domain/vavai/zamer/
shttp://schema.org/
skoshttp://www.w3.org/2004/02/skos/core#
n3http://linked.opendata.cz/ontology/domain/vavai/riv/
n19http://linked.opendata.cz/resource/domain/vavai/vysledek/RIV%2F00216208%3A11320%2F05%3A00001384%21RIV06-MSM-11320___/
n2http://linked.opendata.cz/resource/domain/vavai/vysledek/
rdfhttp://www.w3.org/1999/02/22-rdf-syntax-ns#
n4http://linked.opendata.cz/ontology/domain/vavai/riv/klicoveSlovo/
n10http://linked.opendata.cz/ontology/domain/vavai/riv/duvernostUdaju/
xsdhhttp://www.w3.org/2001/XMLSchema#
n16http://linked.opendata.cz/ontology/domain/vavai/riv/jazykVysledku/
n12http://linked.opendata.cz/ontology/domain/vavai/riv/aktivita/
n15http://linked.opendata.cz/ontology/domain/vavai/riv/druhVysledku/
n13http://linked.opendata.cz/ontology/domain/vavai/riv/obor/
n14http://reference.data.gov.uk/id/gregorian-year/

Statements

Subject Item
n2:RIV%2F00216208%3A11320%2F05%3A00001384%21RIV06-MSM-11320___
rdf:type
skos:Concept n18:Vysledek
dcterms:description
Je ukázáno, že $F$-sigma aditivní systém množin v úplném metrickém prostoru má $\sigma$-diskrétní zjemnění. 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.
dcterms:title
$F$-sigma aditivní systémy množin a invariance borelovských tříd $F\sb \sigma$-additive families and the invariance of Borel classes $F\sb \sigma$-additive families and the invariance of Borel classes
skos:prefLabel
$F\sb \sigma$-additive families and the invariance of Borel classes $F\sb \sigma$-additive families and the invariance of Borel classes $F$-sigma aditivní systémy množin a invariance borelovských tříd
skos:notation
RIV/00216208:11320/05:00001384!RIV06-MSM-11320___
n3:strany
905;915
n3:aktivita
n12:Z n12:P
n3:aktivity
P(GA201/03/0935), P(GP201/03/D120), Z(MSM 113200007)
n3:cisloPeriodika
3
n3:dodaniDat
n14:2006
n3:domaciTvurceVysledku
n6:3116085
n3:druhVysledku
n15:J
n3:duvernostUdaju
n10:S
n3:entitaPredkladatele
n19:predkladatel
n3:idSjednocenehoVysledku
522193
n3:idVysledku
RIV/00216208:11320/05:00001384
n3:jazykVysledku
n16:eng
n3:klicovaSlova
$F\sb; \sigma$-additive; families; invariance; Borel; classes
n3:klicoveSlovo
n4:%5Csigma%24-additive n4:%24F%5Csb n4:Borel n4:classes n4:invariance n4:families
n3:kodStatuVydavatele
US - Spojené státy americké
n3:kontrolniKodProRIV
[191D553B8861]
n3:nazevZdroje
Proceedings of the American Mathematical Society
n3:obor
n13:BA
n3:pocetDomacichTvurcuVysledku
1
n3:pocetTvurcuVysledku
1
n3:projekt
n7:GA201%2F03%2F0935 n7:GP201%2F03%2FD120
n3:rokUplatneniVysledku
n14:2005
n3:svazekPeriodika
133
n3:tvurceVysledku
Spurný, Jiří
n3:zamer
n11:MSM%20113200007
s:issn
0002-9939
s:numberOfPages
11
n17:organizacniJednotka
11320