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

評分☆☆☆☆☆

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

評分☆☆☆☆☆

還沒來得及看。經典書籍推薦一個

評分☆☆☆☆☆

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

評分☆☆☆☆☆

專業，，，，，，，，，，，

評分☆☆☆☆☆

東西不錯，希望一直好用。

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☆☆☆☆☆

送貨速度非常非常快，好評

評分☆☆☆☆☆

這個作者的英語寫的真是太難讀瞭

評分☆☆☆☆☆

買書買吃的穿的用的都在京東。