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Comparison of some notions of \(C^k\)-maps in multi-variable non-archimedian analysis. (English) Zbl 1173.26326

The author compares various definitions of \(C^k\)-maps of open subsets of finite-dimensional vector spaces over a complete valued field. It is shown that the notions of \(C^k\)-maps defined by Schikhof, De Smedt, Bertram, Neeb and the author are identical. Various notions of Hölder differentiable maps are introduced and compared.

MSC:

26E30 Non-Archimedean analysis
26E20 Calculus of functions taking values in infinite-dimensional spaces
46A16 Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.)
46G05 Derivatives of functions in infinite-dimensional spaces
46S10 Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis
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