Geodesic
Implicit functions from locally convex spaces to Banach spaces
Studia Mathematica, Tome 134 (1999) no. 3, pp. 235-250 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We first generalize the classical implicit function theorem of Hildebrandt and Graves to the case where we have a Keller $C_Π^k$-map f defined on an open subset of E×F and with values in F, for E an arbitrary Hausdorff locally convex space and F a Banach space. As an application, we prove that under a certain transversality condition the preimage of a submanifold is a submanifold for a map from a Fréchet manifold to a Banach manifold. 
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     title = {Implicit functions from locally convex spaces to {Banach} spaces},
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Seppo Hiltunen. Implicit functions from locally convex spaces to Banach spaces. Studia Mathematica, Tome 134 (1999) no. 3, pp. 235-250. doi: 10.4064/sm-134-3-235-250

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