拓扑学
Topology
James R. Munkres · 初版 1974 年
11人推荐
19位读者提及
21次提及
为什么值得读
- 严密抽象且被公认为拓扑学领域的黄金标准
- 书中的拓扑与序理论直觉能深度启发软件开发
- 为衔接现代数学和逻辑学打下坚实理论基石
本书为衔接 general topology 与 algebraic topology 课程提供了一本便捷的单本教材资源。全书分为两个独立互异的部分（一部分为 general, point set topology，另一部分为 algebraic topology），每部分均围绕同一组核心基础主题展开，各适合一学期的课程教学。
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……对于愿意投入时间和精力去啃完它的人来说，收获极其巨大。我也推荐下面这三本书，刚好同样覆盖了高等数学的三大主要领域（分析、代数和拓扑）：1. Rudin 的《Principles of Mathematical Analysis》（http://www.amazon.com/Principles-Mathematical-Analysis-Inter...）2. Artin 的《Algebra》（http://www.amazon.com/Algebra-2nd-Featured-Titles-Abstract/d...）……
…extremely rewarding for the people who take the time and effort to go through it. I'd recommend the following three books to similarly cover the three main areas of higher mathematics (analysis, algebra, and topology): 1. Principles of Mathematical Analysis by Rudin (http://www.amazon.com/Principles-Mathematical-Analysis-Inter...) 2. Algebra by Artin (http://www.amazon.com/Algebra-2nd-Featured-Titles-Abstract/d...)…
我是通过 Spivak 的《Calculus》开始接触“真正的”数学的。有些人则是从 Munkres 的《Topology》入门，那本书倒不算难，但非常抽象且严谨，拿来当导引教材很不错。如果你觉得自己微积分底子还可以，也许可以看看 Charles Pugh 的《Real Mathematical Analysis》。……
I got started on "real" math with Spivak's Calculus. Some people start with Topology by Munkres, which is not a difficult book but is very abstract and rigorous so makes a good introduction. If you feel like you have ok calculus chops, maybe Real Mathematical Analysis by Charles Pugh.…
我非常赞同推荐 Munkres 的《Topology》。它基本上算得上是行业黄金标准了。不过，我觉得大三或大四的本科生要是没先上一门分析课的话，看起来会很吃力。严格来说，Munkres 的《Topology》并没有硬性的前置……
I strongly second the recommendation of Munkres' Topology. It's basically the gold standard. However, I think don't think it's accessible to junior/senior undergraduates unless they've taken a prior course in analysis. Technically Munkres' Topology has no formal…
……只要对自己的线性代数感觉良好就行，别觉得非得把每道习题都刷完。另外，我个人特别痴迷序理论（order theory），所以如果你想看点没那么偏代数的内容，可以翻翻 Munkres 的《Topology》。我一直很惊讶于拓扑和序理论的直觉居然能这么频繁地出现在软件开发中。拓扑和逻辑之间有着极深的渊源，所以或许我也不该觉得这么……
…good about your linear algebra; just don't feel like you have to complete every exercise. Also, I'm a sucker for order theory, so if you're up for something a little less algebraic, pick up Munkres' Topology. I'm consistently surprised at how often topological and order-theoretic intuitions come up in software development. There's a close connection between topology and logic, so perhaps I shouldn't be so…
这建议太糟糕了。除了最后一句话以外。更好的建议应该是具体指出该学哪门课。比如说（因为我时间确实不多）：1. 拓扑（Munkres 的书）2. 实分析与测度论（Stein 和 Shakarchi 的系列丛书）3. 代数（Aluffi 的书）4. 线性代数（Friedberg 和 Insel 的书）5. 测度论概率（……的书
This is terrible advice. Apart from the last sentence. A better advice would be to specify which subject to learn. For example, (since I don't really have much time) 1. Topology (book by Munkres) 2. Real Analysis and Measure Theory (book series by Stein Shakarchi) 3. Algebra (book by Aluffi) 4. Linear Algebra (book by Friedberg Insel) 5. Measure Theoretic Probability (book…
……建议在死磕李群（Lie groups）之前先学学这些（如果你还没学过的话）：- 多元微积分（随便一本教材都行）- 微分几何（Manfredo DoCarmo 的三维微分几何）- 拓扑导论（Munkres 的书）。多元微积分能给你一套从形状角度研究曲面的语言，而这正是微分几何要研究的。拓扑则给你提供了更多语言去研究曲面的……
…recommend studying the following before tackling Lie groups (if you haven't yet): -multivariate calculus (any text will do) -differential geometry (Manfredo DoCarmo's diff. geom. in 3D) -introduction to topology (Munkres) Multivariate calculus gives you the language to tackle surfaces in terms of their shape, which is what differential geometry studies. Topology gives you more language to study surfaces in…