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A metric tangential calculus

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Elisabeth Burroni and Jacques Penon

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.

http://www.tac.mta.ca/tac/volumes/23/10/23-10.dvi

http://www.tac.mta.ca/tac/volumes/23/10/23-10.ps

http://www.tac.mta.ca/tac/volumes/23/10/23-10.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/23/10/23-10.dvi

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/23/10/23-10.ps

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