Pseudo-immersions
Annales de l'Institut Fourier, Volume 37 (1987) no. 2, p. 195-221

Let f:(R m ,0)(R n ,0) be a 𝒞 -germ. f is said to be a pseudo-immersion (noted fΨ n,m ) if for continuous germ g:(R,0)(R m ,0), fg𝒞 implies g𝒞 . Ψ n,1 , is completely determined, for each natural n,Ψ 2,2 is shown to coincide with Diff 2 . If K=R or C and g:KK is such that g 2 and g 3 are in 𝒞 . If K=H (field of Hamiltonians), a counter-exemple shows that this implication is no more valid.

Si f est un germe 𝒞 de (R n ,0), on dira que f est une pseudo-immersion (on notera fΨ n,m ) si tous les germes continus g de (R,0) dans (R m ,0), tels que fg𝒞 sont eux-mêmes 𝒞 . On détermine complètement Ψ n,1 , et on montre que Ψ 2,2 = Diff 2 . Par ailleurs, si K=R ou C et si g est une application de K dans K telle que g 2 et g 3 sont 𝒞 , alors g est aussi 𝒞 . Si K=H (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},
     publisher = {Imprimerie Durand},
     address = {28 - Luisant},
     volume = {37},
     number = {2},
     year = {1987},
     pages = {195-221},
     doi = {10.5802/aif.1092},
     zbl = {0596.58004},
     mrnumber = {88e:57028},
     language = {fr},
     url = {http://www.numdam.org/item/AIF_1987__37_2_195_0}
}
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/item/AIF_1987__37_2_195_0/

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