Rationality of semialgebraic functions

Kucharz, Wojciech; Kurdyka, Krzysztof

dc.contributor.author	Kucharz, Wojciech
dc.contributor.author	Kurdyka, Krzysztof
dc.contributor.editor	Krasiński, Tadeusz
dc.contributor.editor	Spodzieja, Stanisław
dc.date.accessioned	2017-12-28T09:11:16Z
dc.date.available	2017-12-28T09:11:16Z
dc.date.issued	2017
dc.identifier.citation	Kucharz W., Kurdyka K., Rationality of semialgebraic functions, [in:] Krasiński T., Spodzieja S. (eds), Analytic and Algebraic Geometry 2, Łódź University Press, Łódź 2017, p. 85-96, doi: 10.18778/8088-922-4.14	pl_PL
dc.identifier.isbn	978-83-8088-922-4
dc.identifier.uri	http://hdl.handle.net/11089/23776
dc.description.abstract	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.	pl_PL
dc.language.iso	en	pl_PL
dc.publisher	Łódź University Press	pl_PL
dc.relation.ispartof	Krasiński T., Spodzieja S. (eds), Analytic and Algebraic Geometry 2, Łódź University Press, Łódź 2017;
dc.rights	Uznanie autorstwa-Użycie niekomercyjne-Bez utworów zależnych 3.0 Polska	*
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/3.0/pl/	*
dc.title	Rationality of semialgebraic functions	pl_PL
dc.type	Book chapter	pl_PL
dc.rights.holder	© Copyright by Authors, Łódź 2017; © Copyright for this edition by Uniwersytet Łódzki, Łódź 2017	pl_PL
dc.page.number	85-96	pl_PL
dc.contributor.authorAffiliation	Institute of Mathematics, Faculty of Mathematics and Computer Science, Jagiellonian University, Łojasiewicza 6, 30-348 Kraków, Poland	pl_PL
dc.contributor.authorAffiliation	Laboratoire de Mathématiques (LAMA), UMR 5127 CNRS Université Savoie Mont Blanc, Campus Scientifique, 73 376 Le Bourget-du-Lac Cedex, France	pl_PL
dc.identifier.eisbn	978-83-8088-923-1
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dc.contributor.authorEmail	Wojciech.Kucharz@im.uj.edu.pl	pl_PL
dc.contributor.authorEmail	Krzysztof.Kurdyka@univ-savoie.fr	pl_PL
dc.identifier.doi	10.18778/8088-922-4.14