拓扑学 [Topology] 下载 mobi epub pdf 电子书 2024

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内容简介

This volume covers approximately the amount of point-set topology that a student who does not intend to specialize in the field should nevertheless know.This is not a whole lot， and in condensed form would occupy perhaps only a small booklet. Our aim， however， was not economy of words， but a lively presentation of the ideas involved， an appeal to intuition in both the immediate and the higher meanings.

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目录

Introduction
1.what is point-set topology about?
2.origin and beginnings
Chapter Ⅰ fundamental concepts
1.the concept of a topological space
2.metric spaces
3.subspaces, disjoint unions and products
4.rases and subbases
5.continuous maps
6.connectedness
7.the hausdorff separation axiom
8.compactness

Chapter Ⅱ topological vector spaces
1.the notion of a topological vector space
2.finite-dimensional vector spaces
3.hilbert spaces
4.banach spaces
5.frechet spaces
6.locally convex topological vector spaces
7.a couple of examples

Chapter Ⅲ the quotient topology
1.the notion of a quotient space
2.quotients and maps
3.properties of quotient spaces
4.examples: homogeneous spaces
5.examples: orbit spaces
6.examples: collapsing a subspace to a point
7.examples: gluing topological spaces together

Chapter Ⅳ completion of metric spaces
1.the completion of a metric space
2.completion of a map
3.completion of normed spaces

Chapter Ⅴ homotopy
1.homotopic maps
2.homotopy equivalence
3.examples
4.categories
5.functors
6.what is algebraic topology?
7.homotopy--what for?
Chapter Ⅵ the two countability axioms
1.first and second countability axioms
2.infinite products
3.the role of the countability axioms
Chapter Ⅶ cw-complexes
1.simplicial complexes
2.cell decompositions
3.the notion of a cw-complex
4.subcomplexes
5.cell attaching
6.why cw-complexes are more flexible
7.yes, but...?

Chapter Ⅷ construction of continuous functions on topological spaces
1.the urysohn lemma
2.the proof of the urysohn lemma
3.the tietze extension lemma
4.partitions of unity and vector bundle sections
5.paracompactness

Chapter Ⅸ covering spaces
1.topological spaces over x
2.the concept of a covering space
3.path lifting
4.introduction to the classification of covering spaces
5.fundamental group and lifting behavior
6.the classification of covering spaces
7.covering transformations and universal cover
8.the role of covering spaces in mathematics

Chapter Ⅹ the theorem of tychonoff
1.an unlikely theorem?
2.what is it good for?
3.the proof
last Chapter
set theory （by theodor br6cker）
references
table of symbols
index

前言/序言

拓扑学 [Topology] 下载 mobi epub pdf txt 电子书 格式

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之前上分析学老师从集合角度出发引出的连续过渡到需要拓扑空间来弥补的地方没听懂，这本书开头就详述了集合和拓扑点的关系，非常到位，观点很细腻，书不厚，就一百五六十页，可以很快读完，但是回味很久。这本书不是普通意义上的教材，作者观点很高但是起点很低，讲解了拓扑学的精到之处，顺手拈来在其他领域的应用，并且恰到好处，尤其是对克莱因瓶的解释很棒，适合有了一定基础又需要整体把握的童鞋们和自学者，推荐。

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包装不错，没有破损；书也是好书。

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就笔者所知，原书作者Klaus Jaenich写过一本著名的微分拓扑方面的教材（原文为德文，后由剑桥大学出版社出版了英文版），还写了好几本风格类似的教科书，包括线性代数、复分析、向量分析，但好像都没有英文版的。

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正在试读中，十五个字啊

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List of books Edit

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好书，快递给力，值得收藏

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2 Combinatorial Rigidity, Jack Graver, Brigitte Servatius, Herman Servatius (1993, ISBN 978-0-8218-3801-3)

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写法独特, 很好的教材

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