2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/171507Let D be a bounded strongly pseudoconvex domain in a Stein manifold S and let Y be a complex manifold. We prove that the graph of any continuous map from the closure of D to Y which is holomorphic in D admits a basis of open Stein neighborhoods in S x Y. Using this we show that many classical spaces of maps from the closure of D to Y which are holomorphic in D are infinite dimensional complex manifolds which are modeled on locally convex topological vector spaces (Banach, Hilbert or Frechet).Complex VariablesFunctional Analysis32E10, 32E30, 32H02, 46G20, 46T10, 54C35, 58B12, 58D15text