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

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

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

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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] epub pdf mobi txt 電子書 下載 2025

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

評分☆☆☆☆☆

3 An Introduction to Gröbner Bases, William W. Adams, Philippe Loustaunau (1994, ISBN 978-0-8218-3804-4)

評分☆☆☆☆☆

評分☆☆☆☆☆

UTM這個係列都很經典。

評分☆☆☆☆☆

這本書不是傳統意義上的拓撲教科書，但對於初學者深入瞭解一般拓撲學具有巨大價值。筆者大約在二十年前曾非常仔細地讀過這本書（至少3遍），是我為數不多的從頭至尾全部閱讀過的書之一。筆者強烈推薦給現在正在學習數學的讀者。

評分☆☆☆☆☆

書中有很多非常漂亮的插圖，而且有不少作者信手拈來的對現代數學概念的直觀但並不膚淺的介紹，如縴維叢、流形嵌入和交換Banach代數等等。記得當時照葫蘆畫瓢地推導瞭Stone-Cech緊化後，一直迷惑不解。直到不久後有一天看到這本書對Banach代數的介紹後突然好像懂瞭，那種奇妙感覺至今難以忘記。除此之外，很多以前學過的概念和理論都是從讀這本書開始真正理解的，如單位分解與仿緊的關係，我沒有見到比這本書寫的更清楚的。

評分☆☆☆☆☆

書中有很多非常漂亮的插圖，而且有不少作者信手拈來的對現代數學概念的直觀但並不膚淺的介紹，如縴維叢、流形嵌入和交換Banach代數等等。記得當時照葫蘆畫瓢地推導瞭Stone-Cech緊化後，一直迷惑不解。直到不久後有一天看到這本書對Banach代數的介紹後突然好像懂瞭，那種奇妙感覺至今難以忘記。除此之外，很多以前學過的概念和理論都是從讀這本書開始真正理解的，如單位分解與仿緊的關係，我沒有見到比這本書寫的更清楚的。

評分☆☆☆☆☆

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

評分☆☆☆☆☆

英文譯本，翻瞭幾頁能讀下去

評分☆☆☆☆☆

還行吧，不錯還行吧，不錯

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