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Revisiting differential calculus in the light of an uncanny function. (English) Zbl 1253.58006

Summary: A metric jet can be linear without being the metric jet of a continuous linear map. We begin with giving such an amazing example and then we get interested in tangentiable maps whose tangent jet at a point is precisely a linear metric jet. For such maps, a local inversion theorem is still true.

MSC:

58C25 Differentiable maps on manifolds
58A20 Jets in global analysis
54E35 Metric spaces, metrizability
18D20 Enriched categories (over closed or monoidal categories)
08B05 Equational logic, Mal’tsev conditions
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References:

[1] E. Burroni, J. Penon, Elements for a metric tangential calculus. http://fr.arxiv.org/abs/0912.1012; E. Burroni, J. Penon, Elements for a metric tangential calculus. http://fr.arxiv.org/abs/0912.1012 · Zbl 1194.58007
[2] Burroni, E.; Penon, J., A metric tangential calculus, TAC, 23, 10 (2010) · Zbl 1194.58007
[3] E. Burroni, J. Penon, Representation of metric jets, Cahiers Top. Géo. Diff. Cat Vol LI-3.; E. Burroni, J. Penon, Representation of metric jets, Cahiers Top. Géo. Diff. Cat Vol LI-3. · Zbl 1228.58005
[4] E. Burroni, J. Penon, Calcul différentiel revisité à la lumière d’une fonction insolite, talk at the SIC in Paris (Oct 2009). http://people.math.jussieu.fr/ guitart/docpp/sic24octobre2009paris.pdf; E. Burroni, J. Penon, Calcul différentiel revisité à la lumière d’une fonction insolite, talk at the SIC in Paris (Oct 2009). http://people.math.jussieu.fr/ guitart/docpp/sic24octobre2009paris.pdf
[5] E. Burroni, J. Penon, Revisiting Differential Calculus in the light of an Uncanny function, talk at the CT2010 in Genova (June 2010). http://ct2010.disi.unige.it/index.php?page=4; E. Burroni, J. Penon, Revisiting Differential Calculus in the light of an Uncanny function, talk at the CT2010 in Genova (June 2010). http://ct2010.disi.unige.it/index.php?page=4 · Zbl 1253.58006
[6] D. Bourn, Baer sums and fibered aspects of Mal’cev operations, Cahiers Top. Géo. Diff. Cat Vol XL-4.; D. Bourn, Baer sums and fibered aspects of Mal’cev operations, Cahiers Top. Géo. Diff. Cat Vol XL-4. · Zbl 0988.18006
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