基础拓扑和几何讲义-教辅教材-文化科教-太极之巅书单号

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基础拓扑和几何讲义内容简介

《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.

基础拓扑和几何讲义本书特色

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 doesnt 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.

基础拓扑和几何讲义目录

chapter some point set topology
1.1naive set theory
1.2topological spaces
1.3connected and compact spaces
1.4continuous functions
1.5product spaces
1.6the tychonoff theorem
chapter 2 more point set topology
2.1separation axioms
2.2separation by continuous functions
2.3more separability
2.4complete metric spaces
2.5applications
chapter 3 fundamental group and covering spaces
3.1homotopy
3.2fundamental group
3.3covering spaces
chapter 4 simplicial complexes
4.1geometry of simplicial complexes
4.2baryccntric subdivisions
4.3simplicial approximation theorem
4.4fundamental group of a simplicial complex
chapter 5 manifolds
5.1differentiable manifolds
5.2differential forms
5.3miscellaneous facts
chapter 6 homology theory and the de rham theory
6.1simplicial homology
6.2do rham's theorem
chapter 7 intrinsic riemannian geometry of surfaces
7.1parallel translation and connections
7.2structural equations and curvature
7.3interpretation of curvature
7.4geodesic coordinate systems
7.5isometrics and spaces of constant curvature
chapter 8 imbedded manifolds in ra
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index