On Nash approximation of complex analytic sets in Runge domains

Abstract

We prove that every complex analytic set X in a Runge domain D can be approximated by Nash sets on relatively compact subdomains of D. We give a necessary and sufficient condition for a complex analytic set X to admit a Nash approximation which coincides with X along its given subsets.

14 pages; Theorem 4.5 added; proof of Proposition 4.2 simplified

References in corpus (3)

• Approximation in C^N
• A Runge approximation theorem for pseudo-holomorphic maps
• Tameness of holomorphic closure dimension in a semialgebraic set