Introduction to Topology

1. Front Matter

   Pages i-xix

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2. Topological Spaces

   • Tej Bahadur Singh

   Pages 1-28

3. Continuity and the Product Topology

   • Tej Bahadur Singh

   Pages 29-50

4. Connectedness

   • Tej Bahadur Singh

   Pages 51-75

5. Convergence

   • Tej Bahadur Singh

   Pages 77-93

6. Compactness

   • Tej Bahadur Singh

   Pages 95-124

7. Topological Constructions

   • Tej Bahadur Singh

   Pages 125-168

8. Countability Axioms

   • Tej Bahadur Singh

   Pages 169-180

9. Separation Axioms

   • Tej Bahadur Singh

   Pages 181-204

10. Paracompactness and Metrizability

    • Tej Bahadur Singh

    Pages 205-218

11. Completeness

    • Tej Bahadur Singh

    Pages 219-233

12. Function Spaces

    • Tej Bahadur Singh

    Pages 235-266

13. Topological Groups

    • Tej Bahadur Singh

    Pages 267-296

14. Transformation Groups

    • Tej Bahadur Singh

    Pages 297-314

15. The Fundamental Group

    • Tej Bahadur Singh

    Pages 315-371

16. Covering Spaces

    • Tej Bahadur Singh

    Pages 373-409

17. Back Matter

    Pages 411-452

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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.

• Fundamental Groups
• Free Groups
• Covering Spaces
• Compact-open Topology
• Transformation Groups
• k-spaces
• Stone-Cech compactification
• Adjunction Spaces

“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)

• Department of Mathematics, University of Delhi, Delhi, India

  Tej Bahadur Singh

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.

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