Topologies on the space of holomorphic functions

Details Topologies on the space of holomorphic functions Topologies on the space of holomorphic functions

2007-07-12

arxiv.org/abs/0707.1876v2

Mathematics

Complex Variables

This is a revision of an earlier version of the paper

Scientific paper

We show that a fairly arbitrary Frechet space topology on the space of holomorphic functions on a domain controls the topology of uniform convergence on compact sets. In fact it turns out that the result we present can be proved more simply using the closed graph theorem. However, we believe that the techniques presented here may be used to prove a more interesting result. Details to appear later.

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