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.
Keywords: differential calculus, jets, metric spaces, categories
2000 MSC: 58C25, 58C20, 58A20, 54E35, 18D20
Theory and Applications of Categories,
Vol. 23, 2010,
No. 10, pp 199-220.