Holomorphically convex domain

Summary

An open set $D \subseteq \C^n$ is holomorphically convex if the holomorphically convex hull of every compact subset of $D$ is again compact. This is the holomorphic analogue of convexity, where hulls are taken with respect to holomorphic functions on $D$ instead of linear functions. For domains in $\C^n$, holomorphic convexity is equivalent to being a domain of holomorphy. On complex manifolds it is one of the conditions defining Stein manifolds.