  Various definitions of C^k-maps on open subsets of finite-dimensional vector
spaces over a complete valued field have been proposed in the literature. We
show that the C^k-maps considered by Schikhof and De Smedt coincide with those
of Bertram, Glockner and Neeb. By contrast, Ludkovsky's C^k-maps need not be
C^k in the former sense, at least in positive characteristic. We also compare
various types of Holder differentiable maps on finite-dimensional and
metrizable spaces.
