發表於2024-11-30
書[0名0]: | 拓撲[0學0](英文版·[0第0]2版)(銷售)[按需印刷]|16509 |
圖書定價: | 120元 |
圖書作者: | (美)James R.Munkres |
齣版社: | 機械工業齣版社 |
齣版日期: | 2004-02-01 0:00:00 |
ISBN號: | 7111136888 |
開本: | 16開 |
頁數: | 537 |
版次: | 2-1 |
內容簡介 |
本書作者在拓撲[0學0][0領0]域享有盛譽。 本書分為兩個[0獨0]立的部分;[0第0]一部分普通拓撲[0學0],講述點集拓撲[0學0]的內容;前4章作為拓撲[0學0]的引論,介紹作為核心題材的集閤論、拓撲空間。連通性、緊性以及可數性和分離性公理;後4章是補充題材;[0第0]二部分代數拓撲[0學0],講述與拓撲[0學0]核心題材相關的主題,其中包括基本群和覆蓋空間及其應用。 本書[0大0]的特點在於對理論的清晰闡述和嚴謹證明,力求讓讀者能夠充分理解。對於疑難的推理證明,將其分解為簡化的步驟,不給讀者留下疑惑。此外,書中還提供瞭[0大0]量練習,可以鞏固加深[0學0]習的效果。嚴格的論證,清晰的條理、豐富的實例,讓深奧的拓撲[0學0]變得輕鬆易[0學0]。 |
目錄 |
Preface A [0No0]te to the Reader Part I GENERAL TOPOLOGY Chapter 1 Set Theory and Logic 1 Fundamental Concepts 2 Functions 3 Relations 4 The Integers and the Real Numbers 5 Cartesian Products 6 Finite Sets 7 Countable and Uncountable Sets 8 The Principle of Recursive Definition 9 Infinite Sets and the Axiom of Choice 10 Well-Ordered Sets 11 The Maximum Principle Supplementary Exercises: Well-Ordering Chapter 2 Topological Spaces and Continuous Functions 12 Topological Spaces 13 Basis for a Topology 14 The Order Topology 15 The Product Topology on X x Y 16 The Subspace Topology 17 Closed Sets and Limit Points 18 Continuous Functions 19 The Product Topology 20 The Metric Topology 21 The Metric Topology (continued) *22 The Quotient Topology *Supplementary Exercises: Topological Groups Chapter 3 Connectedness and Compactness 23 Connected Spaces 24 Connected Subspaces of the Real Line *25 Components and Local Connectedness 26 Compact Spaces 27 Compact Subspaces of the Real Line 28 Limit Point Compactness 29 Local Compactness *Supplementary Exercises: Nets Chapter 4 Countability and Separation Axioms 30 The Countability Axioms 31 The Separation Axioms 32 [0No0]rmal Spaces 33 The Urysohn Lemma 34 The Urysohn Metrization Theorem *35 The Tietze Extension Theorem *36 Imbeddings of Manifolds *Supplementary Exercises: Review of the Basics Chapter 5 The Tycho[0no0]ff Theorem 37 The Tycho[0no0]ff Theorem 38 The Stone-Cech Compactification Chapter 6 Metrization Theorems and Paracompactness 39 Local Finiteness 40 The Nagata-Smir[0no0]v Metrization Theorem 41 Paracompactness 42 The Smir[0no0]v Metrization Theorem Chapter 7 Complete Metric Spaces and Function Spaces 43 Complete Metric Spaces *44 A Space-Filling Curve 45 Compactness in Metric Spaces 46 Pointwise and Compact Convergence 47 Ascoli's Theorem Chapter 8 Baire Spaces and Dimension Theory 48 Baire Spaces *49 A [0No0]where-Differentiable Function 50 Introduction to Dimension Theory *Supplementary Exercises: Loc[0all0]y Euclidean Spaces Part II ALGEBRAIC TOPOLOGY Chapter 9 The Fundamental Group 51 Homotopy of Paths 52 The Fundamental Group 53 Covering Spaces 54 The Fundamental Group of the Circle 55 Retractions and Fixed Points *56 The Fundamental Theorem of Algebra *57 The Borsuk-Ulam Theorem 58 Deformation Retracts and Homotopy Type 59 The Fundamental Group of Sn 60 Fundamental Groups of Some Surfaces Chapter 10 Separation Theorems in the Plane 61 The Jordan Separation Theorem *62 Invariance of Domain 63 The Jordan Curve Theorem 64 Imbedding Graphs in the Plane 65 The Winding Number of a Simple Closed Curve 66 The Cauchy Integral Formula Chapter 11 The Seifert-van Kampen Theorem 67 Direct Sums of Abelian Groups 68 Free Products of Groups 69 Free Groups 70 The Seifert-van Kampen Theorem 71 The Fundamental Group of a Wedge of Circles 72 Adjoining a Two-cell 73 The Fundamental Groups of the Torus and the Dunce Cap Chapter 12 Classification of Surfaces 74 Fundamental Groups of Surfaces 75 Homology of Surfaces 76 Cutting and Pasting 77 The Classification Theorem 78 Constructing Compact Surfaces Chapter 13 Classification of Covering Spaces 79 Equivalence of Covering Spaces 80 The Universal Covering Space *81 Covering Transformations 82 Existence of Covering Spaces *Supplementary Exercises: Topological Properties and Chapter 14 Applications to Group Theory 83 Covering Spaces of a Graph 84 The Fundamental Group of a Graph 85 Subgroups of Free Groups Bibliography Index |
[按需印刷]拓撲學(英文版 第2版) (美)James R.Munkre…|16509 下載 mobi pdf epub txt 電子書 格式 2024
[按需印刷]拓撲學(英文版 第2版) (美)James R.Munkre…|16509 下載 mobi epub pdf 電子書[按需印刷]拓撲學(英文版 第2版) (美)James R.Munkre…|16509 mobi epub pdf txt 電子書 格式下載 2024