Geodesic
A metric tangential calculus
Theory and applications of categories, The Bourn Festschrift, Tome 23 (2010), pp. 199-220.

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

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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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/