The Frolicher--Kriegl differentiabilities as a particular case of the   Bertram--Glockner--Neeb construction
  We prove that the order $k$ differentiability classes for $k=0,1,...\infty$ in the "arc-generated" interpretation of the Lipschitz theory of differentiation by Frolicher and Kriegl can be obtained as particular cases of the general construction by Bertram, Glockner and Neeb leading to $C^k$ differentiabilities from a given $C^0$ concept. 
Seppo I. Hiltunen