Ultrametric and non-locally convex analogues of the general curve lemma of convenient differential calculus

2006/09/01 by Helge Glöckner, Helge Glockner, Glockner, Helge
Mathematics · #26E15 #26E20 #26E30 #45T20 #46A16 #46S10 #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical and Theoretical Analysis #advanced mathematical theories #math.FA #msc:26E15 #msc:26E20 #msc:26E30 #msc:45T20 #msc:46A16 #msc:46S10

paper · pdf · doi:10.48550/arxiv.math/0609040

23 pages, LaTeX

openalex publication_date 2006/09/01 · arxiv created 2007/04/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The General Curve Lemma is a tool of Infinite-Dimensional Analysis, which enables refined studies of differentiability properties of mappings between real locally convex spaces. In this article, we generalize the General Curve Lemma in two ways: First, we remove the condition of local convexity in the real case. Second, we adapt the lemma to the case of curves in topological vector spaces over ultrametric fields.

Citations

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

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