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基本拓撲學（簡體書）
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ISBN13：9787506283458
出版社：世界圖書(北京)出版公司
作者：(英)阿姆斯壯
出版日：2022/07/29
裝訂／頁數：平裝／251頁
規格：22cm*14.8cm (高/寬)
版次：一版
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This is a topology book for undergraduates,and in writing it I have had two aims in mind.Firstly,to make sure the student sees a variety of defferent techniques and applications involving point set,geometric,and algebraic topology,without celving too deeply into any particular area.Secondly,to develop the readers geometrical insight;topology is after all a branch of geometry.本書是一部拓撲學入門書籍，適合作為本科生教程。本書特色:(1)注重培養學生的幾何直觀能力；(2)對於單純同調的處理重點比較突出，使主要線索不至於被複雜的細節所掩蓋；(3)注重抽象理論與具體應用的保持平衡。
目次：導論；連續性；緊性和連通性；同化空間；基礎群；三角剖分；面；單純同調；映射度和Lefschetz 數；結點和複迭空間。
讀者對象：數學專業高年級本科學生、研究生和相關專業的科技人員、教師等。
目次：導論；連續性；緊性和連通性；同化空間；基礎群；三角剖分；面；單純同調；映射度和Lefschetz 數；結點和複迭空間。
讀者對象：數學專業高年級本科學生、研究生和相關專業的科技人員、教師等。
目次
Preface
Chapter 1 Introduction
1.Eulers theorem
2.Topological equivalence
3.Surfaces
4.Abstract spaces
5.A classification theorem
6.Topological 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 connectedness
1.Closed bounded subsets of E
2.The Heine-Borel theorem
3.Properties of compact spaces
4.Product spaces
5.Connectedness
6.Joining points by paths
Chapter 4 Identification spaces
1.Constructing a M/Sbius strip
2.The identification topology
3.Topological groups
4.Orbit spaces
Chapter 5 The fundamental group
1.Homotopic maps
2.Construction of the fundamental group
3.Calculations
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
Chapter 1 Introduction
1.Eulers theorem
2.Topological equivalence
3.Surfaces
4.Abstract spaces
5.A classification theorem
6.Topological 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 connectedness
1.Closed bounded subsets of E
2.The Heine-Borel theorem
3.Properties of compact spaces
4.Product spaces
5.Connectedness
6.Joining points by paths
Chapter 4 Identification spaces
1.Constructing a M/Sbius strip
2.The identification topology
3.Topological groups
4.Orbit spaces
Chapter 5 The fundamental group
1.Homotopic maps
2.Construction of the fundamental group
3.Calculations
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
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