Topology is a large subject with many branches broadly categorized as algebraic topology, point-set topology, and geometric topology. Point-set topology is the main language for a broad variety of mathematical disciplines. Algebraic topology serves as a powerful tool for studying the problems in geometry and numerous other areas of mathematics.
Elements of Topology provides a basic introduction to point-set topology and algebraic topology. It is intended for advanced undergraduate and beginning graduate students with working knowledge of analysis and algebra. Topics discussed include the theory of convergence, function spaces, topological transformation groups, fundamental groups, and covering spaces.
The author makes the subject accessible by providing more than 250 worked examples and counterexamples with applications. The text also includes numerous end-of-section exercises to put the material into context.
Rezensionen / Stimmen
"Each section ends with a carefully composed list of related exercises, and the entire text is interspersed with numerous instructive, directly related examples and counterexamples as well as with many illuminating figures and diagrams. Together with the utmost lucid, detailed, and didactically well-balanced presentation of the material, these special features make the book a suitable source for self-study on the one hand and for a profound course in topology on the other. Both students and instructors can profit a great deal from this excellent primer, which shows the author's rich teaching experience just as much as his expository skills throughout the book."
-Werner Kleinert, Zentralblatt MATH 1273
"I can't think of any significant topic that I would like to see covered in an introductory topology course that is not discussed here. Not only does this book cover the standard examples of quotient spaces and mention applications of Baire category, but it also contains very nice discussions of other topics that I think really enhance such an introductory course. ... all of the extra material included in this book allows for a degree of flexibility that is not present in Simmons [Introduction to Topology and Modern Analysis]. ... The pedagogical value of the book is also enhanced by the presence of quite a number of exercises of varying levels of difficulty and also a substantial number of detailed examples in the text itself. ... This text presents a considerable amount of material in a clear and accessible way and should be carefully considered for textbook adoption by anybody teaching a course in point-set topology."
-Mark Hunacek, MAA Reviews, November 2013
Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
Senior undergraduate and graduate students in topology, especially algebraic topology and point-set topology courses.
Illustrationen
50 s/w Abbildungen
75 Illustrations, black and white
Maße
Höhe: 235 mm
Breite: 156 mm
Gewicht
ISBN-13
978-1-4398-7195-9 (9781439871959)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Autor*in
University of Delhi, India
Topological Spaces
Metric Spaces
Topologies
Derived Concepts
Bases
Subspaces
Continuity and Products
Continuity
Product Topology
Connectedness
Connected Spaces
Components
Path-Connected Spaces
Local Connectivity
Convergence
Sequences
Nets
Filters
Hausdorff Spaces
Countability Axioms
1st and 2nd Countable Spaces
Separable and Lindeloef Spaces
Compactness
Compact Spaces
Countably Compact Spaces
Compact Metric Spaces
Locally Compact Spaces
Proper Maps
Topological Constructions
Quotient Spaces
Identification Maps
Cones, Suspensions and Joins
Wedge Sums and Smash Products
Adjunction Spaces
Coherent Topologies
Separation Axioms
Regular Spaces
Normal Spaces
Completely Regular Spaces
Stone-Cech Compactification
Paracompactness and Metrizability
Paracompact Spaces
A Metrization Theorem
Completeness
Complete Spaces
Completion
Baire Spaces
Function Spaces
Topology of Pointwise Convergence
Compact-Open Topology
Topology of Compact Convergence
Topological Groups
Examples and Basic Properties
Subgroups
Isomorphisms
Direct Products
Transformation Groups
Group Actions
Orbit Spaces
The Fundamental Group
Homotopic Maps
The Fundamental Group
Fundamental Groups of Spheres
The Seifert-van Kampen Theorem
Covering Spaces
Covering Maps
The Lifting Problem
The Universal Covering Spaces
Deck Transformations
The Existence of Covering Spaces
Appendix A: Set Theory
Appendix B: Fields R, C and H
Bibliography
Index
