附註:Includes bibliographical references (pages 217-218) and index.
Preface to the English Edition; Preface; Contents; 1 Introduction; 2 Cutoff and Other Special Smooth Functions on R[sup(n)]; 3 Algebras and Points; 4 Smooth Manifolds (Algebraic Definition); 5 Charts and Atlases; 6 Smooth Maps; 7 Equivalence of Coordinate and Algebraic Definitions; 8 Spectra and Ghosts; 9 The Differential Calculus as a Part of Commutative Algebra; 10 Smooth Bundles; 11 Vector Bundles and Projective Modules; Afterword; Appendix: A.M. Vinogradov Observability Principle, Set Theory and the "Foundations of Mathematics"; References; Index.
摘要:This title is a self-contained introduction to fiber spaces and differential operators on smooth manifolds that is accessible to graduate students specializing in mathematics and physics. The prerequisites for this book are a standard advanced calculus course as well as courses in linear algebra and algebraic structures.
