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

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[德] 亞尼齊 著

齣版社： 世界圖書齣版公司

ISBN：9787510040641

版次：1

商品編碼：10914322

包裝：平裝

外文名稱：Topology

開本：24開

齣版時間：2012-01-01

用紙：膠版紙

頁數：192

正文語種：英文

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

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

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正在試讀中，十五個字啊

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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。

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內容不錯

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就筆者所知，原書作者Klaus Jaenich寫過一本著名的微分拓撲方麵的教材（原文為德文，後由劍橋大學齣版社齣版瞭英文版），還寫瞭好幾本風格類似的教科書，包括綫性代數、復分析、嚮量分析，但好像都沒有英文版的。

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沒破損

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