The convenient setting for Denjoy–Carleman differentiable mappings of Beurling and Roumieu type

@article{Kriegl2011TheCS,
  title={The convenient setting for Denjoy–Carleman differentiable mappings of Beurling and Roumieu type},
  author={Andreas Kriegl and Peter W. Michor and Armin Rainer},
  journal={Revista Matem{\'a}tica Complutense},
  year={2011},
  volume={28},
  pages={549-597}
}
We prove in a uniform way that all Denjoy–Carleman differentiable function classes of Beurling type $$C^{(M)}$$C(M) and of Roumieu type $$C^{\{M\}}$$C{M}, admit a convenient setting if the weight sequence $$M=(M_k)$$M=(Mk) is log-convex and of moderate growth: For $$\mathcal C$$C denoting either $$C^{(M)}$$C(M) or $$C^{\{M\}}$$C{M}, the category of $$\mathcal C$$C-mappings is cartesian closed in the sense that $$\mathcal C(E,\mathcal C(F,G))\cong \mathcal C(E\times F, G)$$C(E,C(F,G))≅C(E×F,G… 
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