Abstract

We show that the converse of the aproximation theorem of Andreotti and Grauert does not hold. More precisely we construct a $4$-complete open subset $D \subset \mathbb{C}^6$ such that the restriction map $H^3 \rightarrow H^3$ has a dense image for every $\mathcal{F} \in Coh$ but the pair $$ is not a $4$-Runge pair