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# Exponential Laws for the Nachbin Ported Topology

Published:2000-06-01
Printed: Jun 2000
• C. Boyd
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## Abstract

We show that for $U$ and $V$ balanced open subsets of (Qno) Fr\'echet spaces $E$ and $F$ that we have the topological identity $$\bigl( {\cal H}(U\times V), \tau_\omega \bigr) = \biggl( {\cal H} \Bigl( U; \bigl( {\cal H}(V), \tau_\omega \bigr) \Bigr), \tau_\omega \biggr).$$ Analogous results for the compact open topology have long been established. We also give an example to show that the (Qno) hypothesis on both $E$ and $F$ is necessary.
 MSC Classifications: 46G20 - Infinite-dimensional holomorphy [See also 32-XX, 46E50, 46T25, 58B12, 58C10] 18D15 - Closed categories (closed monoidal and Cartesian closed categories, etc.) 46M05 - Tensor products [See also 46A32, 46B28, 47A80]