拓撲學 [Topology] 下載 mobi epub pdf 電子書 2025

☆☆☆☆☆
簡體網頁||繁體網頁



下載連結1
下載連結2
下載連結3

類似圖書 點擊查看全場最低價

---

內容簡介

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.

內頁插圖

目錄

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

拓撲學 [Topology] 下載 mobi epub pdf txt 電子書 格式

評分☆☆☆☆☆

好

評分☆☆☆☆☆

正在試讀中，十五個字啊

評分☆☆☆☆☆

好書，快遞給力，值得收藏

評分☆☆☆☆☆

快遞很給力，質量很不錯。

評分☆☆☆☆☆

好書，好好讀……

評分☆☆☆☆☆

還沒來得及看，不是數學專業的，估計很難看懂

評分☆☆☆☆☆

買書買吃的穿的用的都在京東。

評分☆☆☆☆☆

非常不錯,值得細細閱讀,

評分☆☆☆☆☆

之前上分析學老師從集閤角度齣發引齣的連續過渡到需要拓撲空間來彌補的地方沒聽懂，這本書開頭就詳述瞭集閤和拓撲點的關係，非常到位，觀點很細膩，書不厚，就一百五六十頁，可以很快讀完，但是迴味很久。這本書不是普通意義上的教材，作者觀點很高但是起點很低，講解瞭拓撲學的精到之處，順手拈來在其他領域的應用，並且恰到好處，尤其是對剋萊因瓶的解釋很棒，適閤有瞭一定基礎又需要整體把握的童鞋們和自學者，推薦。

類似圖書 點擊查看全場最低價