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

2006/09/01 by Helge Glöckner, Helge Glockner, Glockner, Helge · 1 citation
Computer Science · Mathematics · #26E30 (Primary) 26E20 #46A16 #46G05 #46S10 (Secondary) #FOS: Mathematics #Functional Analysis (math.FA) #General Mathematics (math.GM) #Mathematical Analysis and Transform Methods #Topological and Geometric Data Analysis #advanced mathematical theories #math.FA #math.GM #msc:26E20 #msc:26E30 #msc:46A16 #msc:46G05 #msc:46S10

paper · pdf · doi:10.48550/arxiv.math/0609041

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

arxiv created 2006/09/01 · openalex publication_date 2006/09/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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, 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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