On Nash approximation of complex analytic sets in Runge domains

TL;DR

This paper demonstrates that complex analytic sets within Runge domains can be approximated by Nash sets, providing conditions for when such approximations match the original sets along specified subsets.

Contribution

It establishes a method for approximating complex analytic sets by Nash sets in Runge domains and characterizes when these approximations coincide with the original sets.

Findings

Complex analytic sets in Runge domains can be approximated by Nash sets.

Necessary and sufficient conditions are provided for Nash approximation to match the original set.

Approximation is possible on relatively compact subdomains of the Runge domain.

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.