$Fsb sigma$-additive families and the invariance of Borel classes

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F05%3A00001384" target="_blank" >RIV/00216208:11320/05:00001384 - isvavai.cz</a>

Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

$Fsb sigma$-additive families and the invariance of Borel classes

Original language 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 metricspace 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.

Czech name

$F$-sigma aditivní systémy množin a invariance borelovských tříd

Czech description

Je ukázáno, že $F$-sigma aditivní systém množin v úplném metrickém prostoru má $sigma$-diskrétní zjemnění.

Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

Result was created during the realization of more than one project. More information in the Projects tab.

Continuities

Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year

2005

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Proceedings of the American Mathematical Society

ISSN

0002-9939

e-ISSN

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Volume of the periodical

133

Issue of the periodical within the volume

3

Country of publishing house

US - UNITED STATES

Number of pages

11

Pages from-to

905-915

UT code for WoS article

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EID of the result in the Scopus database

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