Synopses & Reviews
Offering classroom-proven results, Differential Topology
presents an introduction to point set topology via a naive version of nearness space. Its treatment encompasses a general study of surgery, laying a solid foundation for further study and greatly simplifying the classification of surfaces.
This self-contained treatment features 88 helpful illustrations. Its subjects include topological spaces and properties, some advanced calculus, differentiable manifolds, orientability, submanifolds and an embedding theorem, and tangent spaces. Additional topics comprise vector fields and integral curves, surgery, classification of orientable surfaces, and Whitney's embedding theorem. Suitable for advanced undergraduate courses in introductory or differential topology, this volume also serves as a supplementary text in advanced calculus and physics courses, as well as a key source of information for students of mechanics.
Thisand#160;text coversand#160;topological spaces and properties, some advanced calculus, differentiable manifolds, orientability, submanifolds and an embedding theorem, tangent spaces, vector fields and integral curves, Whitney's embedding theorem, more. Includes 88 helpful illustrations. 1982 edition.
An introduction to point set topology for undergraduates, this self-contained text greatly simplifies the complicated subject of the classification of surfaces. Written by a Professor of Mathematics at New Zealand's University of Auckland, it lays a solid foundation for further study.
Originally published: New York: M. Dekker, 1982.
Table of Contents
1. What Is Topology?
2. Topological Spaces
3. Some Topological Properties
4. Some Advanced Calculus
5. Differentiable Manifolds
7. Submanifolds and an Embedding Theorem
8. Tangent Spaces
9. Critical Points Again
10. Vector Fields and Integral Curves
12. The Trace of a Surgery
13. Surgery on a Surface
14. Classification of Orientable Surfaces
15. Whitneyand#8217;s Embedding Theorem
Appendix A. The Unproved Theorems
Appendix B. Further Topics