Let be a -germ. is said to be a pseudo-immersion (noted ) if for continuous germ , implies . , is completely determined, for each natural is shown to coincide with . If or and is such that and are in . If (field of Hamiltonians), a counter-exemple shows that this implication is no more valid.
Si est un germe de , on dira que est une pseudo-immersion (on notera ) si tous les germes continus de dans , tels que sont eux-mêmes . On détermine complètement , et on montre que . Par ailleurs, si ou et si est une application de dans telle que et sont , alors est aussi . Si (corps des hamiloniens) alors cette implication n’est plus vraie.
@article{AIF_1987__37_2_195_0, author = {Joris, Henri and Preissmann, Emmanuel}, title = {Pseudo-immersions}, journal = {Annales de l'Institut Fourier}, pages = {195--221}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {37}, number = {2}, year = {1987}, doi = {10.5802/aif.1092}, mrnumber = {88e:57028}, zbl = {0596.58004}, language = {fr}, url = {http://www.numdam.org/articles/10.5802/aif.1092/} }
TY - JOUR AU - Joris, Henri AU - Preissmann, Emmanuel TI - Pseudo-immersions JO - Annales de l'Institut Fourier PY - 1987 SP - 195 EP - 221 VL - 37 IS - 2 PB - Institut Fourier PP - Grenoble UR - http://www.numdam.org/articles/10.5802/aif.1092/ DO - 10.5802/aif.1092 LA - fr ID - AIF_1987__37_2_195_0 ER -
Joris, Henri; Preissmann, Emmanuel. Pseudo-immersions. Annales de l'Institut Fourier, Volume 37 (1987) no. 2, pp. 195-221. doi : 10.5802/aif.1092. http://www.numdam.org/articles/10.5802/aif.1092/
[1] Analysis on Real and Complex Manifolds, Second edition, Masson, Paris, 1973.
,[2] Une C∞-application non-immersive qui possède la propriété universelle des immersions, Archiv der Mathematik, 39 (1982), 269-277. | MR | Zbl
,[3] Differentiability of a function and of its compositions with functions of one variable, Math. Scand., 20 (1967), 249-268. | MR | Zbl
,[4] Non-linear Conditions for Differentiability of Functions, Journal d'Analyse Math., 45 (1985), 46-68. | MR | Zbl
, , ,[5] Singular Points of Smooth Mappings, Pitman, London, 1979. | MR | Zbl
,[6] Lectures on Expansion Techniques in Algebraic Geometry, Tata Institute, Bombay, 1977. | MR | Zbl
,[7] Commutative Algebra, Vol. II, Van Nostrand, Princeton 1960. | MR | Zbl
, ,[8] Algèbre Commutative, Chap. 7, Hermann, Paris, 1965. | Zbl
,[9] Complex Analysis in One Variable, Birkhäuser, Boston, 1985. | MR | Zbl
,Cited by Sources: