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An axiomatic approach to differentiability on topological groups

✍ Scribed by Helmut Boseck; Klaus-Peter Rudolph

Publisher: John Wiley and Sons
Year: 1980
Tongue: English
Weight: 535 KB
Volume: 98
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.19800980104

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

Starting with a list of “reasonable” properties, called axioms, we are pointing out, that the notion of differentiability is related to the one parameter subgroups of a topological group. This justifies the idea of RISS [5] and the attempts of one of the authors in an earlier paper [1]. In a second part we define differentiable vector valued functions on topological groups. The third part is devoted to a definition of differentiable mappings satisfying the axioms stated before. In this part the considerations are restricted to a rather large class of topological groups including locally compact groups, BANACH LIE groups and current groups.

All topological groups and locally convex topological linear spaces occuring in this paper are assumed to be HAUSDORFF.

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