2007/08/12 by Seppo I. Hiltunen, Hiltunen, Seppo I. · 2 citations
Mathematics · #46E40 (Secondary) #46G05 #46G10 #46T20 #54C05 #54C35 #54D50 (Primary) #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA) #Functional Equations Stability Results #Mathematical and Theoretical Analysis
paper · pdf · doi:10.48550/arxiv.0708.1556
openalex publication_date 2007/08/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
From the point of view of unification of differentiation theory, it is of interest to note that the general construction principle of Bertram, Gloeckner and Neeb leading to a Ck differentiability concept from a given C0 one, besides subsuming the Keller--Bastiani Cck differentiabilities on real Hausdorff locally convex spaces, also does the same to the "arc-generated" interpretation of the Lipschitz theory of differentiation by Frolicher and Kriegl, and likewise to the "compactly generated" theory of Seip's continuous differentiabilities. In this article, we give the details of the proof for the assertion concerning Seip's theory. We also give an example indicating that the premises in Seip's various inverse and implicit function theorems may be too strong in order for these theorems to have much practical value. Also included is a presentation of the BGN--setting reformulated so as to be consistent with the Kelley--Morse--Godel--Bernays--von Neumann type approach to set theory, as well as a treatment of the function space constructions and development of their basic properties needed in the proof of the main result.