A Projective Description of the Nachbin-Ported Topology

In this article we give a projective description of the Nachbin-ported topology tv in H U, X., the space of holomorphic mappings on a balanced open subset U of a Fr´echet space E which satisfies certain general conditions.with values in a Banach space X which is complemented in its bidual. To do this we use the topology t b introduced by Dineen w Math. Scand., 74 1994. 215]236x. As a consequence we characterize when the compact open topology t 0 and tv coincide on H U, X9.for every Banach space X, in terms of a condition on E. Among the techniques we use to obtain these results are the BB-property, the density condition, a version of quasinormability, and Taylor series expansions. Q 1996 Academic Press, Inc.