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