For quasianalytic Denjoy–Carleman differentiable function classes C where the weight sequence Q = (Qk) is log-convex, stable under derivations, of moderate growth and also an L-intersection (see (1.6)), we prove the following: The category of C-mappings is cartesian closed in the sense that C(E, C(F, G)) ∼= C(E × F, G) for convenient vector spaces. Applications to manifolds of mappings are given: The group of C-diffeomorphisms is a regular C-Lie group but not better. Classes of Denjoy-Carleman… CONTINUE READING