Abstract
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, Glöckner 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 Hölder differentiable maps on finite-dimensional and metrizable spaces.
Citation
Helge Glöckner. "Comparison of some notions of Ck-maps in multi-variable non-archimedian analysis." Bull. Belg. Math. Soc. Simon Stevin 14 (5) 877 - 904, December 2007. https://doi.org/10.36045/bbms/1197908901
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