General Topology
General Topology
复制标题
DOI：
10.1142/9789814449342_0009
复制
发表时间：
2008
期刊：
影响因子：
--
通讯作者：
Jesper M. Møller
中科院分区：
文献类型：
--
作者：
Jesper M. Møller
第0章第1章。集合和地图7集合、函数和关系7整数和实数。生成物和副生成物13。有限集和无限集。可数和不可数集合16良序集18 7。部分有序集，极大原理和佐恩引理19第2章。拓扑空间与连续映射232.拓扑空间排序拓扑25产品拓扑25子空间拓扑26。闭集和极限点29 6。连续函数32 7。商拓扑36。度量拓扑43连通空间46紧凑的空间局部紧化空间与Alexandroff紧化58第三章。正则空间和正规空间63可数性公理63分离公理64标准空格66。第二可数正则空间与Urysohn度量化定理[68]。完全正则空间与Stone - Cech紧化[j]。第4章。拓扑空间之间的关系
Contents Chapter 0. Introduction 5 Chapter 1. Sets and maps 7 1. Sets, functions and relations 7 2. The integers and the real numbers 11 3. Products and coproducts 13 4. Finite and infinite sets 14 5. Countable and uncountable sets 16 6. Well-ordered sets 18 7. Partially ordered sets, The Maximum Principle and Zorn's lemma 19 Chapter 2. Topological spaces and continuous maps 23 1. Topological spaces 23 2. Order topologies 25 3. The product topology 25 4. The subspace topology 26 5. Closed sets and limit points 29 6. Continuous functions 32 7. The quotient topology 36 8. Metric topologies 43 9. Connected spaces 46 10. Compact spaces 52 11. Locally compact spaces and the Alexandroff compactification 58 Chapter 3. Regular and normal spaces 63 1. Countability Axioms 63 2. Separation Axioms 64 3. Normal spaces 66 4. Second countable regular spaces and the Urysohn metrization theorem 68 5. Completely regular spaces and the Stone– ˇ Cech compactification 71 6. Manifolds 73 Chapter 4. Relations between topological spaces 75 Bibliography 77 3 CHAPTER 0