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Topology and geometry /
| Autor principal: | |
|---|---|
| Formato: | Libro |
| Lenguaje: | English |
| Publicado: |
New York :
Springer-Verlag,
c1993.
|
| Colección: | Graduate texts in mathematics ;
139 |
| Materias: | |
| Acceso en línea: | Inhaltsverzeichnis Inhaltstext |
Tabla de Contenidos:
- Ch. I. General Topology. 1. Metric Spaces. 2. Topological Spaces. 3. Subspaces. 4. Connectivity and Components. 5. Separation Axioms. 6. Nets (Moore-Smith Convergence). 7. Compactness. 8. Products. 9. Metric Spaces Again. 10. Existence of Real Valued Functions. 11. Locally Compact Spaces. 12. Paracompact Spaces. 13. Quotient Spaces. 14. Homotopy. 15. Topological Groups. 16. Convex Bodies. 17. The Baire Category Theorem
- Ch. II. Differentiable Manifolds. 1. The Implicit Function Theorem. 2. Differentiable Manifolds. 3. Local Coordinates. 4. Induced Structures and Examples. 5. Tangent Vectors and Differentials. 6. Sard's Theorem and Regular Values. 7. Local Properties of Immersions and Submersions. 8. Vector Fields and Flows. 9. Tangent Bundles. 10. Embedding in Euclidean Space. 11. Tubular Neighborhoods and Approximations. 12. Classical Lie Groups. 13. Fiber Bundles. 14. Induced Bundles and Whitney Sums. 15. Transversality. 16. Thom-Pontryagin Theory
- Ch. III. Fundamental Group. 1. Homotopy Groups.