[按需印刷]拓扑学（英文版第2版）（美）James R.Munkre…|16509 下载 mobi epub pdf 电子书 2024

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出版社：机械工业出版社

ISBN：7111136888

商品编码：25201135193

丛书名：经典原版书库

出版时间：2004-02-01

页数：537

图书描述

书[0名0]：	拓扑[0学0]（英文版·[0第0]2版）（销售）[按需印刷]\|16509
图书定价：	120元
图书作者：	（美）James R.Munkres
出版社：	机械工业出版社
出版日期：	2004-02-01 0:00:00
ISBN号：	7111136888
开本：	16开
页数：	537
版次：	2-1

内容简介

本书作者在拓扑[0学0][0领0]域享有盛誉。
本书分为两个[0独0]立的部分；[0第0]一部分普通拓扑[0学0]，讲述点集拓扑[0学0]的内容；前4章作为拓扑[0学0]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公理；后4章是补充题材；[0第0]二部分代数拓扑[0学0]，讲述与拓扑[0学0]核心题材相关的主题，其中包括基本群和覆盖空间及其应用。
本书[0大0]的特点在于对理论的清晰阐述和严谨证明，力求让读者能够充分理解。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[0大0]量练习，可以巩固加深[0学0]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[0学0]变得轻松易[0学0]。

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]拓扑学（英文版第2版）（美）James R.Munkre…|16509 下载 mobi epub pdf txt 电子书格式