从连续有理函数到正则函数

Proceedings of the International Congress of Mathematicians (ICM 2018) Pub Date : 2019-05-01 DOI:10.1142/9789813272880_0075

W. Kucharz, K. Kurdyka

{"title":"从连续有理函数到正则函数","authors":"W. Kucharz, K. Kurdyka","doi":"10.1142/9789813272880_0075","DOIUrl":null,"url":null,"abstract":"Let X be an algebraic set in Rn. Real-valued functions, defined on subsets of X , that are continuous and admit a rational representation have some remarkable properties and applications. We discuss recently obtained results on such functions, against the backdrop of previously developed theories of arc-symmetric sets, arc-analytic functions, approximation by regular maps, and algebraic vector bundles.","PeriodicalId":318252,"journal":{"name":"Proceedings of the International Congress of Mathematicians (ICM 2018)","volume":"44 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"18","resultStr":"{\"title\":\"FROM CONTINUOUS RATIONAL TO REGULOUS FUNCTIONS\",\"authors\":\"W. Kucharz, K. Kurdyka\",\"doi\":\"10.1142/9789813272880_0075\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let X be an algebraic set in Rn. Real-valued functions, defined on subsets of X , that are continuous and admit a rational representation have some remarkable properties and applications. We discuss recently obtained results on such functions, against the backdrop of previously developed theories of arc-symmetric sets, arc-analytic functions, approximation by regular maps, and algebraic vector bundles.\",\"PeriodicalId\":318252,\"journal\":{\"name\":\"Proceedings of the International Congress of Mathematicians (ICM 2018)\",\"volume\":\"44 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-05-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"18\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the International Congress of Mathematicians (ICM 2018)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1142/9789813272880_0075\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the International Congress of Mathematicians (ICM 2018)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/9789813272880_0075","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 18

摘要

设X是Rn中的一个代数集。定义在X的子集上的连续实值函数具有一些显著的性质和应用。我们在弧对称集、弧解析函数、正则映射逼近和代数向量束理论的背景下，讨论了最近得到的关于这些函数的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

FROM CONTINUOUS RATIONAL TO REGULOUS FUNCTIONS

Let X be an algebraic set in Rn. Real-valued functions, defined on subsets of X , that are continuous and admit a rational representation have some remarkable properties and applications. We discuss recently obtained results on such functions, against the backdrop of previously developed theories of arc-symmetric sets, arc-analytic functions, approximation by regular maps, and algebraic vector bundles.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Proceedings of the International Congress of Mathematicians (ICM 2018)

自引率

0.00%

发文量