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Rationality of semialgebraic functions

2017
book section
article
10.18778/8088-922-4.14
Publisher
Uniwersytet Łódzki
80
Author
Kucharz Wojciech

Kurdyka Krzysztof
Editor
Krasiński Tadeusz

Spodzieja Stanisław
Book title / Journal title
Analytic and Algebraic Geometry 2
Place of publication: Publisher
Łódź : Wydawnictwo Uniwersytetu Łódzkiego
Pages
85-96
ISBN
978-83-8088-922-4
eISBN
978-83-8088-923-1
Keywords in English

semialgebraic functions

Bertini theorem

continuous rational functions

Language
English
Book language / Journal language
English
Abstract in English

Let X be an algebraic subset of Rⁿ, and ƒ: X → R a semialgebraic function. We prove that if ƒ is continuous rational on each curve C ⊂ X then: 1) ƒ is arc-analytic, 2) ƒ is continuous rational on X. As a consequence we obtain a characterization of hereditarily rational functions recently studied by J. Kollár and K. Nowak.

Affiliation
Wydział Matematyki i Informatyki : Instytut Matematyki
cris.lastimport.wos2024-04-09T19:05:57Z
dc.abstract.enLet X be an algebraic subset of Rⁿ, and ƒ: X → R a semialgebraic function. We prove that if ƒ is continuous rational on each curve C ⊂ X then: 1) ƒ is arc-analytic, 2) ƒ is continuous rational on X. As a consequence we obtain a characterization of hereditarily rational functions recently studied by J. Kollár and K. Nowak.pl
dc.affiliationWydział Matematyki i Informatyki : Instytut Matematykipl
dc.contributor.authorKucharz, Wojciech - 200567 pl
dc.contributor.authorKurdyka, Krzysztofpl
dc.contributor.editorKrasiński, Tadeuszpl
dc.contributor.editorSpodzieja, Stanisławpl
dc.date.accessioned2018-01-26T13:49:52Z
dc.date.available2018-01-26T13:49:52Z
dc.date.issued2017pl
dc.date.openaccess0
dc.description.accesstimew momencie opublikowania
dc.description.physical85-96pl
dc.description.publication0,55pl
dc.description.versionostateczna wersja wydawcy
dc.identifier.doi10.18778/8088-922-4.14pl
dc.identifier.eisbn978-83-8088-923-1pl
dc.identifier.isbn978-83-8088-922-4pl
dc.identifier.urihttps://ruj.uj.edu.pl/xmlui/handle/item/49356
dc.languageengpl
dc.language.containerengpl
dc.pubinfoŁódź : Wydawnictwo Uniwersytetu Łódzkiegopl
dc.publisher.ministerialUniwersytet Łódzkipl
dc.rightsUdzielam licencji. Uznanie autorstwa - Użycie niekomercyjne - Bez utworów zależnych 3.0 Polska*
dc.rights.licenceCC-BY-NC-ND
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/pl/legalcode*
dc.share.typeinne
dc.sourceinfoliczba autorów 20; liczba stron 188; liczba arkuszy wydawniczych 11,75;pl
dc.subject.ensemialgebraic functionspl
dc.subject.enBertini theorempl
dc.subject.encontinuous rational functionspl
dc.subtypeArticlepl
dc.titleRationality of semialgebraic functionspl
dc.title.containerAnalytic and Algebraic Geometry 2pl
dc.typeBookSectionpl
dspace.entity.typePublication
cris.lastimport.wos
2024-04-09T19:05:57Z
dc.abstract.enpl
Let X be an algebraic subset of Rⁿ, and ƒ: X → R a semialgebraic function. We prove that if ƒ is continuous rational on each curve C ⊂ X then: 1) ƒ is arc-analytic, 2) ƒ is continuous rational on X. As a consequence we obtain a characterization of hereditarily rational functions recently studied by J. Kollár and K. Nowak.
dc.affiliationpl
Wydział Matematyki i Informatyki : Instytut Matematyki
dc.contributor.authorpl
Kucharz, Wojciech - 200567
dc.contributor.authorpl
Kurdyka, Krzysztof
dc.contributor.editorpl
Krasiński, Tadeusz
dc.contributor.editorpl
Spodzieja, Stanisław
dc.date.accessioned
2018-01-26T13:49:52Z
dc.date.available
2018-01-26T13:49:52Z
dc.date.issuedpl
2017
dc.date.openaccess
0
dc.description.accesstime
w momencie opublikowania
dc.description.physicalpl
85-96
dc.description.publicationpl
0,55
dc.description.version
ostateczna wersja wydawcy
dc.identifier.doipl
10.18778/8088-922-4.14
dc.identifier.eisbnpl
978-83-8088-923-1
dc.identifier.isbnpl
978-83-8088-922-4
dc.identifier.uri
https://ruj.uj.edu.pl/xmlui/handle/item/49356
dc.languagepl
eng
dc.language.containerpl
eng
dc.pubinfopl
Łódź : Wydawnictwo Uniwersytetu Łódzkiego
dc.publisher.ministerialpl
Uniwersytet Łódzki
dc.rights*
Udzielam licencji. Uznanie autorstwa - Użycie niekomercyjne - Bez utworów zależnych 3.0 Polska
dc.rights.licence
CC-BY-NC-ND
dc.rights.uri*
http://creativecommons.org/licenses/by-nc-nd/3.0/pl/legalcode
dc.share.type
inne
dc.sourceinfopl
liczba autorów 20; liczba stron 188; liczba arkuszy wydawniczych 11,75;
dc.subject.enpl
semialgebraic functions
dc.subject.enpl
Bertini theorem
dc.subject.enpl
continuous rational functions
dc.subtypepl
Article
dc.titlepl
Rationality of semialgebraic functions
dc.title.containerpl
Analytic and Algebraic Geometry 2
dc.typepl
BookSection
dspace.entity.type
Publication
Affiliations
Wydział Matematyki i Informatyki
Kucharz, Wojciech
No affiliation
Kurdyka, Krzysztof
Krasiński, Tadeusz
Spodzieja, Stanisław

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Except as otherwise noted, this item is licensed under : Udzielam licencji. Uznanie autorstwa - Użycie niekomercyjne - Bez utworów zależnych 3.0 Polska

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