| 《基础拓扑和几何讲义》介绍了：The exciting revelations thatthere is some unity in mathematics, that fields overlap, that techniques of onefield have applications in another, are denied the undergraduate. He mustwait until he is well into graduate work to see interconnections, presumablybecause earlier he doesn‘t know enough.These notes are an attempt to break up this compartmentalization, at leastin topologygeometry. What the student has learned in algebra and advancedcalculus are used to prove some fairly deep results relating geometry, topology, and group theory. |
| 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 |
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