In mathematics, more precisely in complex analysis, the holomorphically convex hull of a given compact set in the n-dimensional complex space Cn is defined as follows. Let be a domain (an open and connected set), or alternatively for a more general definition, let be an dimensional complex analytic manifold. Further let stand for the set of holomorphic functions on For a compact set , the holomorphically convex hull of is (One obtains a narrower concept of polynomially convex hull by requiring in the above definition that f be a polynomial.) The domain is called holomorphically convex if for every , When