Seip's differentiability concepts as a particular case of the Bertram--Gloeckner--Neeb construction
| Autor: | Hiltunen, Seppo I. |
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| Rok vydání: | 2007 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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 C^k differentiability concept from a given C^0 one, besides subsuming the Keller--Bastiani C_c^k 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. Comment: Comments: 32 pages, AmSLaTeX; versions 2--7: correction of misprints and minor mistakes, improvement of unhappy wordings, Proposition "C_{Se0} is BGN" added on page 22 in v2, (7) "locality" added to Proposition 47(=v1:46) in v3 |
| Databáze: | arXiv |
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