On Nash approximation of complex analytic sets in Runge domains期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

On Nash approximation of complex analytic sets in Runge domains

Authors:	Janusz Adamus Marcin Bilski

Affiliation:	1. Department of Mathematics, The University of Western Ontario, London, Ontario N6A 5B7, Canada;2. Institute of Mathematics, Faculty of Mathematics and Computer Science, Jagiellonian University, ul. ?ojasiewicza 6, 30-348 Kraków, Poland

Abstract:	We prove that every complex analytic set X in a Runge domain Ω can be approximated by Nash sets on any relatively compact subdomain _Ω₀ $Ω_{0}$ of Ω. Moreover, for every Nash subset Y of Ω with Y⊂X $Y \subset X$ , the approximating sets can be chosen so that they contain Y∩_Ω₀ $Y \cap Ω_{0}$ . As a consequence, we derive a necessary and sufficient condition for a complex analytic set X to admit a Nash approximation which coincides with X along its arbitrary given subset.

Keywords:	Analytic set Runge domain Approximation Nash set
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