...there are reasons enough to warrant a coherent treatment of the main body of differential topology in the realm of Banach manifolds, which is at the same time correct and complete. This book fills the gap: whenever possible the manifolds treated are Banach manifolds with corners. Corners add to the complications and the authors have carefully fathomed the validity of all main results at corners. Even in finite dimensions some results at corners are more complete and better thought out here than elsewhere in the literature. The proofs are correct and with all details. I see this book as a reliable monograph of a well-defined subject; the possibility to fall back to it adds to the feeling of security when climbing in the more dangerous realms of infinite dimensional differential geometry.
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CHAPTER 2 THE WHITNEY EXTENSION THEOREM AND THE INVERSE MAPPING THEOREM FOR DIFFERENTIABLE MANIFOLDS WIT...
CHAPTER 3 SUBMANIFOLDS AND IMMERSIONS
CHAPTER 4 SUBMERSIONS AND QUOTIENT MANIFOLDS
CHAPTER 5 SUBIMMERSIONS
CHAPTER 6 LIE GROUPS
CHAPTER 7 TRANSVERSALITY
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admits a topological chart c=(U class p-1 closed embedding closed linear subspace closed set compact set consider the map continuous map converges Corollary defined denoted dense diffeomorphism of class differentiable manifold differentiable structure equivalence relation exists an open finite dimensional Fredholm map function of class Hence Hilbert space immersion of class inclusion map injective map Jº x,x ke|Nu Let f Let G Let us consider Lie group Lindelöf linear continuous map linear homeomorphism linear subspace linearly independent system locally finite family manifold of class map f map of class measure zero Moreover ne|N open set paracompact space partitions of unity Proof Let proper map quadrant real Banach space real Hilbert space statements are equivalent subimmersion submanifold of class submersion of class surjective map system of elements theorem topological space topology Twſp totally neat submanifold transversal