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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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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图书质量很好，下次还会来买！

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学习数学基础，温故而知新

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

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这本书不是传统意义上的拓扑教科书，但对于初学者深入了解一般拓扑学具有巨大价值。笔者大约在二十年前曾非常仔细地读过这本书（至少3遍），是我为数不多的从头至尾全部阅读过的书之一。笔者强烈推荐给现在正在学习数学的读者。

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拓扑学的一本入门书籍，买来仔细学习

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好薄一本，略贵呀，凑单用的...

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老古董书籍 哈哈哈哈哈哈哈

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东西不错

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