Exponential Laws for the Nachbin Ported Topology

Boyd, C.

Canadian mathematical bulletin, Tome 43 (2000) no. 2, pp. 138-144

Résumé

We show that for $U$ and $V$ balanced open subsets of $\left( \text{Qno} \right)$ Fréchet spaces $E$ and $F$ that we have the topological identity $$\text{(}\mathcal{H}(U\times V),{{\tau }_{\omega }})=\left( \mathcal{H}\left( U;\left( \mathcal{H}(V),{{\tau }_{\omega }} \right) \right),{{\tau }_{\omega }} \right).$$ Analogous results for the compact open topology have long been established. We also give an example to show that the $\left( \text{Qno} \right)$ hypothesis on both $E$ and $F$ is necessary.

Détail

DOI : 10.4153/CMB-2000-021-x

Mots-clés : 46G20, 18D15, 46M05

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