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

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

☆☆☆☆☆
简体网页||繁体网页



点击这里下载

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

类似图书 点击查看全场最低价

---

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.

内页插图

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] epub pdf mobi txt 电子书 下载 2024

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

评分☆☆☆☆☆

List of books Edit

评分☆☆☆☆☆

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。

评分☆☆☆☆☆

The book I've surveyed which includes Janich's Intro to Differential Topology, Isham's Differential Geometry for Physicists, Differential Manifold by Serge Lang, Introduction to Manifolds by Tu L.W. unfortunately all reads like books written by mathematicians for mathematicians and has a dearth of physical examples and visual aids. Tu L.W.'s Intro to Manifold is surprisingly soft handed and perhaps would be good for a first book. The book nonetheless lacks motivating examples and il

评分☆☆☆☆☆

老古董书籍 哈哈哈哈哈哈哈

评分☆☆☆☆☆

Springer的书必属经典

评分☆☆☆☆☆

好好好好好好

评分☆☆☆☆☆

还行吧，不错还行吧，不错

评分☆☆☆☆☆

评分☆☆☆☆☆

不错，活动时买的，满减后值了，以后还是要多关注京东的活动

类似图书 点击查看全场最低价