Implicit functions from locally convex spaces to Banach spaces

Volume 134 / 1999

Seppo Hiltunen Studia Mathematica 134 (1999), 235-250 DOI: 10.4064/sm-134-3-235-250


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.


  • Seppo Hiltunen

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