基础拓扑和几何讲义

《基础拓扑和几何讲义》内容为：At the present time, the average undergraduate mathematics major findsmathematics heavily compartmentalized. After the calculus, he takes a coursein analysis and a course in algebra. Depending upon his interests （or those ofhis department）, he takes courses in special topics. If he is exposed to topology,it is usually straightforward point set topology; if he is exposed to geometry, it is usually classical differential geometry.

Chapter Some point set topology 1.1 Naive set theory 1.2 Topological spaces 1.3 Connected and compact spaces 1.4 Continuous functions 1.5 Product spaces 1.6 The Tychonoff theorem Chapter 2 More point set topology 2.1 Separation axioms 2.2 Separation by continuous functions 2.3 More separability 2.4 Complete metric spaces 2.5 Applications Chapter 3 Fundamental group and covering spaces 3.1 Homotopy 3.2 Fundamental group 3.3 Covering spaces Chapter 4 Simplicial complexes 4.1 Geometry of simplicial complexes 4.2 Baryccntric subdivisions 4.3 Simplicial approximation theorem 4.4 Fundamental group of a simplicial complex Chapter 5 Manifolds 5.1 Differentiable manifolds 5.2 Differential forms 5.3 Miscellaneous facts Chapter 6 Homology theory and the De Rham theory 6.1 Simplicial homology 6.2 Do Rham's theorem Chapter 7 Intrinsic Riemannian geometry of surfaces 7.1 Parallel translation and connections 7.2 Structural equations and curvature 7.3 Interpretation of curvature 7.4 Geodesic coordinate systems 7.5 Isometrics and spaces of constant curvature Chapter 8 Imbedded manifolds in Ra Bibliography Index

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  来源：豆瓣 发布时间：2025-05-17 08:29:29