# Complex curves in pseudoconvex Runge domains containing discrete subsets

## TL;DR

This paper proves that in any pseudoconvex Runge domain in c2b2, every closed discrete set can be contained in a properly embedded complex curve with any topology, extending the understanding of complex curves in such domains.

## Contribution

It establishes the existence of properly embedded complex curves with arbitrary topology containing any given discrete set in pseudoconvex Runge domains.

## Key findings

- Any closed discrete subset in a pseudoconvex Runge domain can be contained in a properly embedded complex curve.
- The complex curve can have any prescribed topology, including infinite.
- The result extends the class of known complex curves in pseudoconvex domains.

## Abstract

For any pseudoconvex Runge domain $\Omega\subset\mathbb{C}^2$ we prove that every closed discrete subset in $\Omega$ is contained in a properly embedded complex curve in $\Omega$ with any prescribed topology (possibly infinite).