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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)
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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)
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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)
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skos:notation
| - RIV/00216208:11320/05:00001384!RIV06-MSM-11320___
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http://linked.open.../vavai/riv/strany
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http://linked.open...avai/riv/aktivita
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http://linked.open...avai/riv/aktivity
| - P(GA201/03/0935), P(GP201/03/D120), Z(MSM 113200007)
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http://linked.open...iv/cisloPeriodika
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http://linked.open...vai/riv/dodaniDat
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http://linked.open...aciTvurceVysledku
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http://linked.open.../riv/druhVysledku
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http://linked.open...iv/duvernostUdaju
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http://linked.open...titaPredkladatele
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http://linked.open...dnocenehoVysledku
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http://linked.open...ai/riv/idVysledku
| - RIV/00216208:11320/05:00001384
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http://linked.open...riv/jazykVysledku
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http://linked.open.../riv/klicovaSlova
| - $F\sb; \sigma$-additive; families; invariance; Borel; classes (en)
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http://linked.open.../riv/klicoveSlovo
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http://linked.open...odStatuVydavatele
| - US - Spojené státy americké
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http://linked.open...ontrolniKodProRIV
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http://linked.open...i/riv/nazevZdroje
| - Proceedings of the American Mathematical Society
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http://linked.open...in/vavai/riv/obor
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http://linked.open...ichTvurcuVysledku
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http://linked.open...cetTvurcuVysledku
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http://linked.open...vavai/riv/projekt
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http://linked.open...UplatneniVysledku
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http://linked.open...v/svazekPeriodika
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http://linked.open...iv/tvurceVysledku
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http://linked.open...n/vavai/riv/zamer
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issn
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number of pages
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http://localhost/t...ganizacniJednotka
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