Comparison of some notions of C^k-maps in multi-variable non-archimedian analysis

Details Comparison of some notions of C^k-maps in multi-variable non-archimedian analysis Comparison of some notions of C^k-maps in multi-variable non-archimedian analysis

2006-09-01

arxiv.org/abs/math/0609041v1

Mathematics

Functional Analysis

extended preprint version (46 pages) with additional appendices B and C

Scientific paper

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.

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