拓扑学：第2版

图书标准信息

• 作者 [美]默可雷斯 著
• 出版社 机械工业出版社
• 出版时间 2004-02
• 版次 1
• ISBN 9787111136880
• 定价 59.00元
• 装帧 平装
• 开本 其他
• 纸张 胶版纸
• 页数 537页
• 原版书名 Topology
• 丛书 经典原版书库

【内容简介】

　　本书分为两个独立的部分。第一部分普通拓扑学，讲述点集拓扑学的内容：前4章作为拓扑学的引论，介绍作为核心题材的集合论、拓扑空间、连通性、紧性以及可数性和分离性分理；后4章是补充题材。第二部分代数拓扑学，讲述与拓扑学核心题材相关的主题，其中包括基本群和覆盖安闪及其应用。
　　本书最大的特点在于对理论的清晰阐述和严谨证明，力求证读者能够充分理解。对于疑难的推理证明，将其分解为简化的步骤，不给读者留下疑惑。此外，书中还提供了大量练习，可以巩固深学习的效果。严格的论证、清晰的条理、丰富的实例，让深奥的拓扑学变得轻松易学。

【目录】

preface
anotetothereader
partigeneraltopology
chapter1settheoryandlogic
1fundamentalconcepts
2functions
3relations
4theintegersandtherealnumbers
5cartesianproducts
6finitesets
7countableanduncountablesets
8theprincipleofrecursivedefinition
9infinitesetsandtheaxiomofchoice
10well-orderedsets
11themaximumprinciple
supplementaryexercises：well-ordering

chapter2topologicalspacesandcontinuousfunctions
12topologicalspaces
13basisforatopology
14theordertopology
.15theproducttopologyonxxy
16thesubspacetopology
17closedsetsandlimitpoints
18continuousfunctions
19theproducttopology
20themetrictopology
21themetrictopology（continued）
22thequotienttopology
supplementaryexercises：topologicalgroups

chapter3connectednessandcompactness
23connectedspaces
24connectedsubspacesoftherealline
*25componentsandlocalconnectedness
26compactspaces
27compactsubspacesoftherealline
28limitpointcompactness
29localcompactness
supplementaryexercises：nets

chapter4countabilityandseparationaxioms
30thecountabilityaxioms
31theseparationaxioms
32normalspaces
33theurysohnlemma
34theurysohnmetrizationtheorem
35thetietzeextensiontheorem
36imbeddingsofmanifolds
supplementaryexercises：reviewofthebasics

chapter5thetychonofftheorem
37thetychonofftheorem
38thestone-cechcompactification

chapter6metrizationtheoremsandparacompactness
39localfiniteness
40thenagata-smirnovmetrizationtheorem
41paracompactness
42thesmirnovmetrizationtheorem

chapter7completemetricspacesandfunctionspaces
43completemetricspaces
44aspace-fillingcurve
45compactnessinmetricspaces
46pointwiseandcompactconvergence
47ascoli'stheorem

chapter8bairespacesanddimensiontheory
48bairespaces
49anowhere-differentiablefunction
50introductiontodimensiontheory
supplementaryexercises：locallyeuclideanspaces
partiialgebraictopology

chapter9thefundamentalgroup
51homotopyofpaths
52thefundamentalgroup
53coveringspaces
54thefundamentalgroupofthecircle
55retractionsandfixedpoints
56thefundamentaltheoremofalgebra
57theborsuk-ulamtheorem
58deformationretractsandhomotopytype
59thefundamentalgroupofsn
60fundamentalgroupsofsomesurfaces

chapter10separationtheoremsintheplane
61thejordanseparationtheorem
62invarianceofdomain
63thejordancurvetheorem
64imbeddinggraphsintheplane
65thewindingnumberofasimpleclosedcurve
66thecauchyintegralformula

chapter11theseifert-vankampentheorem
67directsumsofabeliangroups
68freeproductsofgroups
69freegroups
70theseifert-vankampentheorem
71thefundamentalgroupofawedgeofcircles
72adjoiningatwo-cell
73thefundamentalgroupsofthetorusandtheduncecap

chapter12classificationofsurfaces
74fundamentalgroupsofsurfaces
75homologyofsurfaces
76cuttingandpasting
77theclassificationtheorem
78constructingcompactsurfaces

chapter13classificationofcoveringspaces
79equivalenceofcoveringspaces
80theuniversalcoveringspace
81coveringtransformations
82existenceofcoveringspaces
supplementaryexercises：topologicalpropertiesand

chapter14applicationstogrouptheory
83coveringspacesofagraph
84thefundamentalgroupofagraph
85subgroupsoffreegroups
bibliography
index