作者：Guoling Wang
页数：152
出版社：高等教育出版社
出版日期：2019
ISBN：9787040527490
电子书格式：pdf/epub/txt
内容简介
本书内容包括映射的连续性、拓扑空间的连通性和紧性及分离公理和可数公理。本书的大部分内容既适用于一年级本科生，又会使希望学习一般拓扑学的基本概念、例子和习题的研究生和数学家感兴趣。
本书作者王国亮为北京理工大学副教授，本书完稿于作者在麻省理工学院(MIT)的访问期间。
本书特色
本书内容包括映射的连续性、拓扑空间的连通性和紧性及分离公理和可数公理。本书的大部分内容既适用于一年级本科生，又会使希望学习一般拓扑学的基本概念、例子和习题的研究生和数学家感兴趣。本书作者王国亮为北京理工大学副教授，本书完稿于作者在麻省理工学院（MIT）的访问期间。
目录
Chapter 1 Introduction
Exercises 1
Selected Solutions 1
Chapter 2 Topological Spaces
2.1.Topological structures
2.2.Subspace topology
2.3.Covers
2.4.Point position with respect to a set
2.5.Metrics and the metric topology
Exercises 2
Selected Solutions 2
Chapter 3 Continuous Maps and Homeomorphisms
3.1.Continuous maps
3.2.Homeomorphisms
3.3.Topological properties
Exercises 3
Selected Solutions 3
Chapter 4 Connectedness
4.1.Connected spaces
4.2.Path-Connectedness
Exercises 4
Selected Solutions 4
Chapter 5 Separation and Countability Axioms
5.1.Axioms To, T1, T2, T3, and T4
5.2.Hausdorff spaces
5.3.Regular spaces and normal spaces
5.4.Countability axioms
Exercises 5
Selected Solutions 5
Chapter 6 Compactness
6.1.Compact spaces
6.2.Interaction of compactness with other topological properties
6.3.Gromov-Hausdorff distance
Exercises 6
Selected Solutions 6
Chapter 7 Product Spaces and Quotient Spaces
7.1.Product spaces
7.2.Quotient spaces
Exercises 7
Selected Solutions 7
Appendix A Some Elementary Inequalities
Bibliography
Author Index
Subject Index
Exercises 1
Selected Solutions 1
Chapter 2 Topological Spaces
2.1.Topological structures
2.2.Subspace topology
2.3.Covers
2.4.Point position with respect to a set
2.5.Metrics and the metric topology
Exercises 2
Selected Solutions 2
Chapter 3 Continuous Maps and Homeomorphisms
3.1.Continuous maps
3.2.Homeomorphisms
3.3.Topological properties
Exercises 3
Selected Solutions 3
Chapter 4 Connectedness
4.1.Connected spaces
4.2.Path-Connectedness
Exercises 4
Selected Solutions 4
Chapter 5 Separation and Countability Axioms
5.1.Axioms To, T1, T2, T3, and T4
5.2.Hausdorff spaces
5.3.Regular spaces and normal spaces
5.4.Countability axioms
Exercises 5
Selected Solutions 5
Chapter 6 Compactness
6.1.Compact spaces
6.2.Interaction of compactness with other topological properties
6.3.Gromov-Hausdorff distance
Exercises 6
Selected Solutions 6
Chapter 7 Product Spaces and Quotient Spaces
7.1.Product spaces
7.2.Quotient spaces
Exercises 7
Selected Solutions 7
Appendix A Some Elementary Inequalities
Bibliography
Author Index
Subject Index
