Introduction to Topology

by Tej Bahadur Singh

Overview

Topology is a large subject with several branches, broadly categorized as algebraic topology, point-set topology, and geometric topology. Point-set topology is the main language for a broad range of mathematical disciplines, while algebraic topology offers as a powerful tool for studying problems in geometry and numerous other areas of mathematics. This book presents the basic concepts of topology, including virtually all of the traditional topics in point-set topology, as well as elementary topics in algebraic topology such as fundamental groups and covering spaces. It also discusses topological groups and transformation groups. When combined with a working knowledge of analysis and algebra, this book offers a valuable resource for advanced undergraduate and beginning graduate students of mathematics specializing in algebraic topology and harmonic analysis.

Product Details

ISBN-13:	9789811369568
Publisher:	Springer Nature Singapore
Publication date:	05/03/2019
Edition description:	1st ed. 2019
Pages:	452
Product dimensions:	6.10(w) x 9.25(h) x (d)

About the Author

TEJ BAHADUR SINGH is an Emeritus Professor at the Department of Mathematics, University of Delhi, India, which he joined in 1989. Earlier, he served at the University of Allahabad and Atarra P.G. College, Banda, India. He received his Ph.D. from the University of Allahabad in 1983. With more than 40 years of teaching experience, he has written several research articles on the cohomological theory of compact transformation groups and has successfully guided eight M.Phil. and Ph.D. students. His primary research interest is in algebraic topology. He has taught various courses, including point-set topology, field theory, module theory, representation of finite groups, algebra, calculus, geometry, linear algebra, and real analysis.

Table of Contents

Chapter 1. Topological Spaces.- Chapter 2. Continuity and Products.- Chapter 3. Connectedness.- Chapter 4. Convergence.- Chapter 5. Countability axioms.- Chapter 6. Compactness.- Chapter 7. Topological Constructions.- Chapter 8. Separation Axioms.- Chapter 9. Paracompactness and Metrisability.- Chapter 10. Completeness.- Chapter 11. Function Spaces.- Chapter 12. Topological Groups.- Chapter 13. Transformation Groups.- Chapter 14. The fundamental Group.- Chapter 15. Covering Spaces.

Editorial Reviews

It is suitable for senior undergraduate and beginning graduate students of mathematics. … Each chapter contains numerous examples and exercises, making this book an interesting and useful reference for any basic course in topology.” (Fabio Ferrari Ruffino, Mathematical Reviews, 2019)

“It can be used as a consultation book by students of mathematics or other people interested in topology.” (F.G.Lupiáñez, European Mathematical Society, euro-math-soc.eu, October 23, 2019)

“This is a textbook on basic general topology and a small part of algebraic topology intended for undergraduate students and first level graduate students. … the book may be also useful to those who teach topological courses.” (Ljubiša D. Kočinac, zbMATH 1426.54001, 2020)

“This book would make a good choice for a graduate course in point-set (with an introduction to algebraic) topology, and would also function well as a text for a fairly sophisticated undergraduate course.” (Mark Hunacek, MAA Reviews, August 11, 2019)

From the Publisher