出版时间:2004-2 出版社:机械工业 作者:[美]James R.Munkres 页数:537
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内容概要
本书分为两个独立的部分。第一部分普通拓扑学,讲述点集拓扑学的内容:前4章作为拓扑学的引论,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分理;后4章是补充题材。第二部分代数拓扑学,讲述与拓扑学核心题材相关的主题,其中包括基本群和覆盖安闪及其应用。
本书最大的特点在于对理论的清晰阐述和严谨证明,力求证读者能够充分理解。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,书中还提供了大量练习,可以巩固深学习的效果。严格的论证、清晰的条理、丰富的实例,让深奥的拓扑学变得轻松易学。
书籍目录
PrefaceA Note to the ReaderPart 1 GENERAL TOPOLOGYChapter 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-OrderingChapter 2 Topological Spaces and Continuous Functions 12 Topological Saces 13 Basis for a Topology 14 The Order Topology 15 The Product Topology on 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 Mertic Topology(continued) *22 The Quotient Topology *Supplementary Exercises:Topological Groups……
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