This introduction to topology provides separate, in-depth coverage of both general topology and algebraic topology. Includes many examples and figures. GENERAL TOPOLOGY. Set Theory and Logic. Topological Spaces and Continuous Functions. Connectedness and Compactness. Countability and Separation Axioms. The Tychonoff Theorem. Metrization Theorems and paracompactness. C...
This introduction to topology provides separate, in-depth coverage of both general topology and algebraic topology. Includes many examples and figures. GENERAL TOPOLOGY. Set Theory and Logic. Topological Spaces and Continuous Functions. Connectedness and Compactness. Countability and Separation Axioms. The Tychonoff Theorem. Metrization Theorems and paracompactness. Complete Metric Spaces and Function Spaces. Baire Spaces and Dimension Theory. ALGEBRAIC TOPOLOGY. The Fundamental Group. Separation Theorems. The Seifert-van Kampen Theorem. Classification of Surfaces. Classification of Covering Spaces. Applications to Group Theory. For anyone needing a basic, thorough, introduction to general and algebraic topology and its applications.
These examples suggest that an answer to the mathematician’s riddle: “How is a set different from a door?” should be: “A door must be either open or closed, and cannot be both, while a set can be open, or closed, or both, or neither!” (查看原文)
大黄蜂95号
机械工业出版社2006版
0 有用 Eric Zhou 2017-01-26 20:52:47
好书，看了point set topology部分，然而在经济学中的应用并不多。私以为许多和拓扑相关的题目早就被上古时代的大神们（e.g. Arrow，Debrue）搞定了。
0 有用 丁白 2022-02-21 23:16:43
点集拓扑非常之详细，可以和尤承业配合使用（munkres阅读，尤承业当定理手册）。深感这门课应该和数分2/3同时学（去掉代拓），这样能为分析学概念提供更为统一和直观的理解（个人感觉可数性部分写的极妙
11 有用 Welfare 2014-04-26 05:26:56
3t option. T: QA 611 .M82 2000 requested recall & e: http://www.maths.ed.ac.uk/~aar/papers/munkres2.pdf Solutions: http://www.uio.no/studier/emner/matnat/math/MAT4500/h11/undervisningsmateriale/Links%... 3t option. T: QA 611 .M82 2000 requested recall & e: http://www.maths.ed.ac.uk/~aar/papers/munkres2.pdf Solutions: http://www.uio.no/studier/emner/matnat/math/MAT4500/h11/undervisningsmateriale/Links%20to%20solutions http://dbfin.com/2010/11/2000-munkres-topology-solutions-chapter-1/ http://www.math.cornell.edu/~matsumura/math4530/math4530web.h (展开)
1 有用 Mixolydian 2017-03-27 14:54:32
point set方面Munkres是不二之选。Part 2 algebraic topology写得一般，照着Massey的书写，写得还没有Massey好...
0 有用 谁家的鸡 2021-08-24 09:14:30
很久没看过点集拓扑了，为了学习几何找这本复习一下。