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ULTRAMETRIC AND NON-LOCALLY CONVEX ANALOGUES OF THE GENERAL CURVE LEMMA OF CONVENIENT DIFFERENTIAL CALCULUS
HELGE GLÖCKNER
Journal:

Glasgow Mathematical Journal / Volume 50 / Issue 2 / May 2008

Published online by Cambridge University Press:

01 May 2008, pp. 271-288

Print publication:

May 2008
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The General Curve Lemma is a tool of Infinite-Dimensional Analysis that enables refined studies of differentiability properties of maps between real locally convex spaces to be made. 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.