About this product

Product Identifiers

PublisherCengage Learning Asia

ISBN-109812432884

ISBN-139789812432889

eBay Product ID (ePID)44475656

Product Key Features

Number of Pages324 Pages

Publication NamePrinciples of Topology

LanguageEnglish

Publication Year2002

SubjectFinite Mathematics, Topology

TypeTextbook

Subject AreaMathematics

AuthorFred H. Croom

FormatTrade Paperback

Dimensions

Item Weight18 Oz

Additional Product Features

Intended AudienceCollege Audience

Dewey Edition23

Dewey Decimal514

Table Of ContentPreface CHAPTER 1. INTRODUCTION 1.1 The Nature of Topology. 1.2 The Origin of Topology. 1.3 Preliminary Ideas from Set Theory 1.4 Operations on Sets: Union, Intersection, and Difference. 1.5 Cartesian Products. 1.6 Functions. 1.7 Equivalence Relations. CHAPTER 2. THE LINE AND THE PLANE 2.1 Upper and Lower Bounds. 2.2 Finite and Infinite Sets. 2.3 Open Sets and Closed Sets on the Real Line 2.4 The Nested Intervals Theorem. 2.5 The Plane. Suggestions for Further Reading. Historical Notes for Chapter 2. CHAPTER 3. METRIC SPACES 3.1 The Definition and Some Examples. 3.2 Open Sets and Closed Sets in Metric Spaces. 3.3 Interior, Closure, and Boundary. 3.4 Continuous Metric Spaces. Suggestions for Further Reading. Historical Notes for Chapter 3. CHAPTER 4. TOPOLOGICAL SPACES 4.1 The Definition and Some Examples. 4.2 Interior, Closure, and Boundary. 4.3 Basis and Subbasis. 4.4 Continuity and Topological Equivalence. 4.5 Subspaces. Suggestions for Further Reading. Historical Notes for Chapter 4. CHAPTER 5. CONNECTEDNESS 5.1 Connectedness and Disconnectness Spaces. 5.2 Theorem on Connectedness. 5.3 Connected Subsets of the Real Line. 5.4 Applications of Connectedness. 5.5 Path Connected Spaces. 5.6 Locally Connected and Locally Path Connected Spaces. Suggestions for Further Reading. Historical Notes for Chapter 5. CHAPTER 6. COMPACTNESS 6.1 Compact Spaces and Subspaces. 6.2 Compactness and Continuity. 6.3 Properties Related to Compactness. 6.4 One-Point Compactification. 6.5 The Cantor Set. Suggestions for Further Reading. Historical Notes for Chapter 6. CHAPTER 7. PRODUCT AND QUOTIENT SPACES 7.1 Finite Products. 7.2 Arbitrary Products. 7.3 Comparision of Topology. 7.4 Quotient Spaces. 7.5 Surfaces and Manifolds. Suggestions for Further Reading. Historical Notes for Chapter 7. CHAPTER 8. SEPARATION PROPERTIES AND METRIZATION 8.1 T0, T1, and T2-Spaces. 8.2 Regular Spaces. 8.3 Normal Spaces. 8.4 Separation by Continuity Functions. 8.5 Metrization. 8.6 The Stone-Cech Compactification. Suggestions for Further Reading. Historical Notes for Chapter 8. CHAPTER 9. THE FUNDAMENTAL GROUP 9.1 The Nature of Algebraic Topology. 9.2 The Fundamental Group. The Fundamental Group of S1. 9.4 Additional Examples of Fundamentals Groups. 9.5 The Brouwer Fixed Point Theorem and Related Results. 9.6 Categories and Functors. Suggestions for Further Reading. Historical Notes for Chapter 9. APPENDIX: INTRODUCTION TO GROUPS Bibliography Index

SynopsisThis text presents the fundamental principles of topology rigorously but not abstractly. It emphasizes the geometric nature of the subject and the applications of topological ideas to geometry and mathematical analysis.The usual topics of point-set topology, including metric spaces, general topological spaces, continuity, topological equivalence, basis, sub-basis, connectedness , compactness, separation properties, metrization, subspaces, product spaces, and quotient spaces are treated in this text.Most of the factual information about topology presented in this text is stated in the theorems and illustrated in the accompanying examples, figures and exercises. This book contains many exercises of varying degrees of difficulty. The notation used in this text is reasonably standard; a list of symbols with definitions appears on the front end-sheets.This text is designed for a one-semester introduction to topology at the undergraduate and beginning graduate levels. It is accessible to junior mathematics majors who have studied multivariable calculus., This text presents the fundamental principles of topology rigorously but not abstractly. It emphasizes the geometric nature of the subject and the applications of topological ideas to geometry and mathematical analysis. The usual topics of point-set topology, including metric spaces, general topological spaces, continuity, topological equivalence, basis, sub-basis, connectedness , compactness, separation properties, metrization, subspaces, product spaces, and quotient spaces are treated in this text. Most of the factual information about topology presented in this text is stated in the theorems and illustrated in the accompanying examples, figures and exercises. This book contains many exercises of varying degrees of difficulty. The notation used in this text is reasonably standard; a list of symbols with definitions appears on the front end-sheets. This text is designed for a one-semester introduction to topology at the undergraduate and beginning graduate levels. It is accessible to junior mathematics majors who have studied multivariable calculus.