Differential Topology, Volumen173Elsevier, 1992 M06 2 - 603 páginas ...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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Contenido
CHAPTER 1 REAL DIFFERENTIABLE MANIFOLDS WITH CORNERS | 1 |
CHAPTER 2 THE WHITNEY EXTENSION THEOREM AND THE INVERSE MAPPING THEOREM FOR DIFFERENTIABLE MANIFOLDS WIT... | 73 |
CHAPTER 3 SUBMANIFOLDS AND IMMERSIONS | 113 |
CHAPTER 4 SUBMERSIONS AND QUOTIENT MANIFOLDS | 159 |
CHAPTER 5 SUBIMMERSIONS | 215 |
CHAPTER 6 LIE GROUPS | 283 |
CHAPTER 7 TRANSVERSALITY | 309 |
CHAPTER 8 PARAMETRIZED THEOREMS OF THE DENSITY OF THE TRANSVERSALITY | 345 |
CHAPTER 9 SPACES OF DIFFERENTIABLE MAPS | 427 |
CHAPTER 10 APPROXIMATION OF DIFFERENTIABLE MAPS | 523 |
CHAPTER 11 OPENNESS AND DENSITY OF THE TRANSVERSALITY | 543 |
BIBLIOGRAPHY | 575 |
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admits a topological chart class p+1 class peNu 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 E₁ exists an open finite dimensional Fredholm map function of class Hence Hilbert space immersion of class inclusion map injective map integer Let f:X→X Let us consider Let X,X Lie group Lindelöf linear continuous map linear homeomorphism linear subspace linearly independent system locally finite family manifold of class map of class measure zero Moreover open neighbourhood open set P₁ P₂ paracompact space partitions of unity proper map quadrant real Banach space real Hilbert space statements are equivalent subimmersion submanifold of class submersion of class Suppose system of elements Tf(x Theorem topological space totally neat submanifold transversal U₁ x'eX