The Frolicher--Kriegl differentiabilities as a particular case of the Bertram--Glockner--Neeb construction

2008/04/27 by Seppo I. Hiltunen, Hiltunen, Seppo I. · 1 citation
Mathematics · #46A17 (Secondary) #46G05 (Primary) #46T20 #58C20 #58C25 #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Geometric and Algebraic Topology #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.0804.4273

openalex publication_date 2008/04/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the order k differentiability classes for k=0,1,...∞ in the "arc-generated" interpretation of the Lipschitz theory of differentiation by Frolicher and Kriegl can be obtained as particular cases of the general construction by Bertram, Glockner and Neeb leading to C^k differentiabilities from a given C⁰ concept.

Citations

• Seip's differentiability concepts as a particular case of the Bertram--Gloeckner--Neeb construction

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