Maps between Frechet spaces

Can one give the set of maps between two Frechet spaces the structure of a Frechet or locally convex space? If so, with which topology? Thanks in advance for your answers,

Intergalakti

• I'm not entirely sure what you expect. "All maps", from a topological point of view, is pretty wild. What topology would you give to the set of all maps $\mathbb R\to\mathbb R$? – Martin Argerami May 19 at 18:18
• The compact-open topology would be quite natural (by maps, I obviously mean morphisms in the category of Frechet spaces). The maps from a normed to a Banach space also form a Banach space, and I think one could prove that the continuous maps from a topol. VS that is countable at infinity to a Frechet space is Frechet with that topology – Intergalakti May 20 at 16:32