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29 March 2024
 
  » arxiv » 0912.1012

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Elements for a metric tangential calculus
Elisabeth Burroni ; Jacques Penon ;
Date 5 Dec 2009
AbstractThe metric jets, introduced in the first chapter, generalize the jets (at order one) of Charles Ehresmann. In short, for a "good" map $f$ (said to be "tangentiable" at $a$), we define its metric jet tangent at $a$ (composed of all the maps which are locally lipschitzian at $a$ and tangent to $f$ at $a$) called the "tangential" of $f$ at $a$, and denoted T$f_a$ (the domain and codomain of $f$ being metric spaces).
Furthermore, guided by the heuristic example of the metric jet T$f_a$, tangent to a map $f$ differentiable at $a$, which can be canonically represented by the unique continuous affine map it contains, we will extend, in the second chapter, into a specific metric context, this property of representation of a metric jet.This yields a lot of relevant examples of such representations.
Source arXiv, 0912.1012
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