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
装帧平装
货号35
上书时间2024-10-31
商品详情
- 品相描述:八五品
-
品相如图
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
点击展开
点击收起
— 没有更多了 —
品相如图
以下为对购买帮助不大的评价