Geodesic
A metric tangential calculus
Theory and applications of categories, The Bourn Festschrift, Tome 23 (2010), pp. 199-220 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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The metric jets, introduced here, generalize the jets (at order one) of Charles Ehresmann. In short, for a ``good'' map f (said to be ``tangentiable'' at a) between metric spaces, 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 Tf_a. So, in this metric context, we define a ``new differentiability'' (called ``tangentiability'') which extends the classical differentiability (while preserving most of its properties) to new maps, traditionally pathologic.

Classification : 58C25, 58C20, 58A20, 54E35, 18D20
Keywords: differential calculus, jets, metric spaces, categories 
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     author = {Elisabeth Burroni and Jacques Penon},
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     volume = {23},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2010_23_a9/}
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Elisabeth Burroni; Jacques Penon. A metric tangential calculus. Theory and applications of categories, The Bourn Festschrift, Tome 23 (2010), pp. 199-220. http://geodesic.mathdoc.fr/item/TAC_2010_23_a9/