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基本拓扑学
《基本拓扑学(英文版)》主要内容:This is a topology book for undergraduates,and in writing it I have had two aims in mind.Firstly,to make sure the student sees a variety of defferent techniques and applications involving point set,geometric,and algebraic topology,without celving too deeply into any particular area.Secondly,to develop the reader's geometrical insight;topology is after all a branch of geometry. -
Topology
This introduction to topology provides separate, in-depth coverage of both general topology and algebraic topology. Includes many examples and figures. GENERAL TOPOLOGY. Set Theory and Logic. Topological Spaces and Continuous Functions. Connectedness and Compactness. Countability and Separation Axioms. The Tychonoff Theorem. Metrization Theorems and paracompactness. Complete Metric Spaces and Function Spaces. Baire Spaces and Dimension Theory. ALGEBRAIC TOPOLOGY. The Fundamental Group. Separation Theorems. The Seifert-van Kampen Theorem. Classification of Surfaces. Classification of Covering Spaces. Applications to Group Theory. For anyone needing a basic, thorough, introduction to general and algebraic topology and its applications. -
Topology
This introduction to topology provides separate, in-depth coverage of both general topology and algebraic topology. Includes many examples and figures. GENERAL TOPOLOGY. Set Theory and Logic. Topological Spaces and Continuous Functions. Connectedness and Compactness. Countability and Separation Axioms. The Tychonoff Theorem. Metrization Theorems and paracompactness. Complete Metric Spaces and Function Spaces. Baire Spaces and Dimension Theory. ALGEBRAIC TOPOLOGY. The Fundamental Group. Separation Theorems. The Seifert-van Kampen Theorem. Classification of Surfaces. Classification of Covering Spaces. Applications to Group Theory. For anyone needing a basic, thorough, introduction to general and algebraic topology and its applications. -
基础拓扑学讲义
《基础拓扑学讲义》是拓扑学的入门教材。内容包括点集拓扑与代数拓扑,重点介绍代数拓扑学中的基本概念、方法和应用。共分八章:拓扑空间的基本概念,紧致性和连通性,商空间与闭曲面,同伦与基本群,复叠空间,单纯同调及其应用,映射度与不动点等。每节配备了适量习题并在书末附有解答与提示。《基础拓扑学讲义》叙述深入浅出,例题丰富,论证严谨,重点突出;强调几何背景,注意培养学生的几何直观能力;方法新颖,特别是关于对径映射的映射度的计算颇具新意。 -
拓扑学
本书作者在拓扑学领域享有盛誉。 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公理;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空间及其应用。 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,书中还提供了大量练习,可以巩固加深学习的效果。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。 -
代数拓扑的微分形式
代数拓扑的微分形式,ISBN:9787506201124,作者:(美)Raoul Bott,(美)Loring W.Tu著