Implicit functions from locally convex spaces to Banach spaces
Tom 134 / 1999
Studia Mathematica 134 (1999), 235-250
DOI: 10.4064/sm-134-3-235-250
Streszczenie
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.
