J. Aust. Math. Soc.  78 (2005), 273-290
Topologies on spaces of vector-valued meromorphic functions

Enrique Jordá
  Departamento de Matemática Aplicada
  E. Politécnica Superior de Alcoy
  Universidad Politécnica de Valencia
  Plaza Ferrándiz y Carbonell 2
  E-03801 Alcoy (Alicante)

This paper presents two natural extensions of the topology of the space of scalar meromorphic functions $M(\Omega)$ described by Grosse-Erdmann in 1995 to spaces of vector-valued meromorphic functions $M(\Omega,E)$. When $E$ is locally complete and does not contain copies of $\omega$ we compare these topologies with the topology induced by the representation $M(\Omega,E)\simeq M(\Omega)\varepsilon E$ recently obtained by Bonet, Maestre and the author.
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