We prove that a Mergelyan-type approximation theorem holds true for holomorphic mappings to the manifold C2\ R2: Given a compact subset K of C such that C\ K is connected, and a continuous f map from K to C2\ R2 which is holomorphic in the interior of K, there exists holomorphic mappings fn from C to C2\ R2 whose restrictions to K converge uniformly to f.
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