THE CONVENIENT SETTING OF GLOBAL ANALYSIS

By PATRICIA WILLIAMS

CHAPTER I CALCULUS OF SMOOTH MAPPINGS 1 SMOOTH CURVES 2 COMPLETENESS 3 SMOOTH MAPPINGS AND THE EXPONENTIAL LAW 4 THE C?-TOPOLOGY 5 UNIFORM BOUNDEDNESS PRINCIPLES AND MULTILINEARITY 6 SOME SPACES OF SMOOTH FUNCTIONS HISTORICAL REMARKS ON SMOOTH CALCULUS CHAPTER II CALCULUS OF HOLOMORPHIC AND REAL ANALYTIC MAPPINGS 7 CALCULUS OF HOLOMORPHIC MAPPINGS 8 SPACES OF HOLOMORPHIC MAPPINGS AND GERMS 9 REAL ANALYTIC CURVES 10 REAL ANALYTIC MAPPINGS 11 THE REAL ANALYTIC EXPONENTIAL LAW HISTORICAL REMARKS ON HOLOMORPHIC AND REAL ANALYTIC CALCULUS CHAPTER III PARTITIONS OF UNITY 12 DI?ERENTIABILITY OF FINITE ORDER 13 DI?ERENTIABILITY OF SEMINORMS 14 SMOOTH BUMP FUNCTIONS 15 FUNCTIONS WITH GLOBALLY BOUNDED DERIVATIVES 16 SMOOTH PARTITIONS OF UNITY AND SMOOTH NORMALITY CHAPTER IV SMOOTHLY REALCOMPACT SPACES 17 BASIC CONCEPTS AND TOPOLOGICAL REALCOMPACTNESS 18 EVALUATION PROPERTIES OF HOMOMORPHISMS 19 STABILITY OF SMOOTHLY REALCOMPACT SPACES 20 SETS ON WHICH ALL FUNCTIONS ARE BOUNDED CHAPTER V EXTENSIONS AND LIFTINGS OF MAPPINGS 21 EXTENSION AND LIFTING PROPERTIES 22 WHITNEY’S EXTENSION THEOREM REVISITED 23 FR¨OLICHER SPACES AND FREE CONVENIENT VECTOR SPACES 24 SMOOTH MAPPINGS ON NON-OPEN DOMAINS 25 REAL ANALYTIC MAPPINGS ON NON-OPEN DOMAINS 26 HOLOMORPHIC MAPPINGS ON NON-OPEN DOMAINS CHAPTER VI IN?NITE DIMENSIONAL MANIFOLDS 27 DI?ERENTIABLE MANIFOLDS 28 TANGENT VECTORS 29 VECTOR BUNDLES 30 SPACES OF SECTIONS OF VECTOR BUNDLES 31 PRODUCT PRESERVING FUNCTORS ON MANIFOLDS CHAPTER VII CALCULUS ON IN?NITE DIMENSIONAL MANIFOLDS 32 VECTOR FIELDS 33 DI?ERENTIAL FORMS 34 DE RHAM COHOMOLOGY 35 DERIVATIONS ON DI?ERENTIAL FORMS AND THE FR¨OLICHER-NIJENHUIS BRACKET CHAPTER VIII IN?NITE DIMENSIONAL DI?ERENTIAL GEOMETRY 36 LIE GROUPS 37 BUNDLES AND CONNECTIONS 38 REGULAR LIE GROUPS 39 BUNDLES WITH REGULAR STRUCTURE GROUPS 40 RUDIMENTS OF LIE THEORY FOR REGULAR LIE GROUPS CHAPTER IX MANIFOLDS OF MAPPINGS 41 JETS AND WHITNEY TOPOLOGIES 42 MANIFOLDS OF MAPPINGS 43 DI?EOMORPHISM GROUPS 44 PRINCIPAL BUNDLES WITH STRUCTURE GROUP A DI?EOMORPHISM GROUP 45 MANIFOLDS OF RIEMANNIAN METRICS 46 THE KORTEWEG – DE VRIES EQUATION AS A GEODESIC EQUATION COMPLEMENTS TO MANIFOLDS OF MAPPINGS CHAPTER X FURTHER APPLICATIONS 47 MANIFOLDS FOR ALGEBRAIC TOPOLOGY 48 WEAK SYMPLECTIC MANIFOLDS 49 APPLICATIONS TO REPRESENTATIONS OF LIE GROUPS 50 APPLICATIONS TO PERTURBATION THEORY OF OPERATORS 51 THE NASH-MOSER INVERSE FUNCTION THEOREM 52 APPENDIX: FUNCTIONAL ANALYSIS 53 APPENDIX: PROJECTIVE RESOLUTIONS OF IDENTITY ON BANACH SPACES REFERENCES