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Elements of Topology, by Tej Bahadur Singh
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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.
- Sales Rank: #3184475 in Books
- Published on: 2013-05-20
- Original language: English
- Number of items: 1
- Dimensions: 9.25" h x 6.25" w x 1.00" l, .0 pounds
- Binding: Hardcover
- 552 pages
Review
"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
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