Ansemil, José María M.Ponte, Socorro2023-06-202023-06-202007-10-15R.A. Aron, Entire functions of unbounded type on a Banach space, Boll. Unione Mat. Ital. (4) 9 (1974) 28–31. S.B. Chae, Holomorphy and Calculus in Normed Spaces, Monographs and Textbooks in Pure and Appl. Math., vol. 92, Marcel Dekker, 1985. S. Dineen, Complex Analysis in Locally Convex Spaces, North-Holland Math. Stud., vol. 57, 1981. S. Dineen, Complex Analysis on Infinite Dimensional Spaces, Springer Monogr. Math., 1999. J. Horváth, Topological Vector Spaces and Distributions, Addison–Wesley, Reading, MA, 1966. B. Josefson, Weak sequential convergence in the dual of a Banach space does not imply norm convergence, Ark. Mat. 13 (1975) 79–89. G. Köthe, Topological Vector Spaces II, Springer, Berlin, 1979. J. Mujica,Gérmenes holomorfos y funciones holomorfas en espacios de Fréchet, Publicaciones del Departamento de Teoría de Funciones, Universidad de Santiago, Spain, 1978. J. Mujica, Spaces of germs of holomorphic functions, in: Studies in Analysis, Adv. Math. 4 (Suppl. Stud.) (1979) 1–41. J. Mujica, Spaces of holomorphic mappings on Banach spaces with a Schauder basis, Studia Math. 122 (2) (1997) 139–151.0022-247X10.1016/j.jmaa.2007.01.012https://hdl.handle.net/20.500.14352/50151In this paper we prove, among other things, that the space of all holomorphic functions on an open subset U of a complex metrizable space E, endowed with the Nachbin ported topology, is metrizable only if E has finite dimension. This answers a question by Mujica in [J. Mujica, Germenes holomorfos y funciones holomorfas en espacios de Frechet, Publicaciones del Departamento de Teoria de Funciones, Universidad de Santiago, Spain, 1978].engjournal articlehttp://www.sciencedirect.com/science/article/pii/S0022247X07000339http://www.sciencedirect.com/restricted access517.98holomorphic functionnachbin topologymetrizable spaceFunciones (Matemáticas)1202 Análisis y Análisis Funcional