基本拓扑学

《基本拓扑学》是2008年1月1日世界图书出版公司出版的图书，作者是(英国)阿姆来自斯壮。

• 书名 基本拓扑学
• 作者 (英国)阿姆斯壮
• ISBN 9787506283458
• 页数 251
• 出版社 世界图书出版公司

内容简介

　　This is a topology book for un来自dergradua360百科tes,and in writi干斗矿利稳ng it I have had two aims i种依烟n mind.Firstl才植哥兴免果源低并将频y,to make sure the student sees a variety of defferent techniques and applications involving point set,geometric,and al乡即接察苦皮联肉车gebraic t频孔工车阳止opology,with形差毛哥保落out celving too deeply into any particular area.Secondly,to develop the reader's geometrical insight;topolog限虽题果轮额y is after all a branch of geometry.

图书目录

　　Preface

　　Chapter 1 Introduction

　　1.Euler's theorem

　　2.Topological equivalence

　　3.Surfaces

　　4.Abstract 风成引走严跑送赶spaces

　　5.A classification theore才器施益读叫汉增响更m

　　6.Topol术武责运厚期场觉ogical invariants

　　Chapter 2 Continuity

　　1.Open and closed sets

　　2.Continuous functions

　　3.A space-filling curve

　　4.The Tietze extension theorem

　　Chapter 3 Compactness and conn洋境敌养完计高ectedness

　别诉和己刑　1.Closed bounded subsets of E"

　　2.The Heine-Borel theorem

　　3.Properties o个系空德手把房员f compact spaces

　　4.Product spaces

　　自使差女色握输翻药陈级5.Connectedness

　　6.Joining points by paths

　　C画名hapter 4 Identification spaces

　　1.Constructing a M/Sbius strip

　　2.The identification t令专内对屋opology

　　3.Topological groups

　　4.Orbit spaces

　　Chapter 5 The fundamental group

　　1班高海管更棉.Homotopic maps

　　2.Construction of the fundamental group

　　3.C空alculations

　　4.Homotopy type

　　5.The Brouwer fixed-point theorem

　　6.Separation of the plane

　　7.The boundary of a surface

　　Chapter 6 Triangulations

　　1.Triangulating spaces

　　2.Barycentric subdivision

　　3.Simplicial approximation

　　4.The edge group of a complex

　　5.Triangulating orbit spaces

　　6.Infinite complexes

　　Chapter 7 Surfaces

　　1.Classification

　　2.Triangulation and orientation

　　3.Euler characteristics

　　4.Surgery

　　5.Surface symbols

　　Chapter 8 Simplicial homology

　　1.Cycles and boundaries

　　2.Homology groups

　　3.Examples

　　4.Simplicial maps

　　5.Stellar subdivision

　　6.Invariance

　　Chapter 9 Degree and Lefschetz number

　　1.Maps of spheres

　　2.The Euler-Poincar6 formula

　　3.The Borsuk-Ulam theorem

　　4.The Lefschetz fixed-point theorem

　　5.Dimension

　　Chapter 10 Knots and covering spaces

　　1.Examples of knots

　　2.The knot group

　　3.Seifert surfaces

　　4.Covering spaces

　　5.The Alexander polynomial

　　Appendix: Generators and relations

　　Index