Exponential Laws for the Nachbin Ported Topology

http://dx.doi.org/10.4153/CMB-2000-021-x
Canad. Math. Bull. 43(2000), 138-144

  Published:2000-06-01
 Printed: Jun 2000

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.