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Geometry of Bounded Frechet Manifolds
In this paper we develop the geometry of bounded Fr\'echet manifolds. We
prove that a bounded Fr\'echet tangent bundle admits a vector bundle structure.
But the second order tangent bundle of a bounded Fr\'echet manifold ,
becomes a vector bundle over if and only if is endowed with a linear
connection. As an application, we prove the existence and uniqueness of the
integral curve of a vector field on
Sard's theorem for mappings between Fr\'echet manifolds
In this paper we prove an infinite-dimensional version of Sard's theorem for
Fr\'{e}chet manifolds.
Let and be bounded Fr\'{e}chet manifolds such that the topologies
of their model Fr\'{e}chet spaces are defined by metrics with absolutely convex
balls.
Let be an -Lipschitz-Fredholm map with k >
\max \lbrace {\Ind f,0} \rbrace . Then the set of regular values of is
residual in
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