Introduction to Topology / by Tej Bahadur Singh.
- 1st ed. 2019.
- Singapore : Springer Singapore : Imprint: Springer, 2019.
- Mathematics and Statistics (Springer-11649)
1 online resource (XIX, 452 pages) : 93 illustrations
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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.
- 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.
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- Publisher Number:
- 10.1007/978-981-13-6954-4 doi
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