General Topology for Beginners
Seiten
2025
Cambridge University Press (Verlag)
978-1-009-50588-8 (ISBN)
Cambridge University Press (Verlag)
978-1-009-50588-8 (ISBN)
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This book on general topology is meant for graduate and senior undergraduate mathematics students. Written in a lucid manner, the text is enriched with examples, exercises, and proofs. Each topic has been explained in detail, and proofs are presented in a stepwise manner, which makes it suitable for self-study.
This textbook focuses on general topology. Meant for graduate and senior undergraduate mathematics students, it introduces topology thoroughly from scratch and assumes minimal basic knowledge of real analysis and metric spaces. It begins with thought-provoking questions to encourage students to learn about topology and how it is related to, yet different from, geometry. Using concepts from real analysis and metric spaces, the definition of topology is introduced along with its motivation and importance. The text covers all the topics of topology, including homeomorphism, subspace topology, weak topology, product topology, quotient topology, coproduct topology, order topology, metric topology, and topological properties such as countability axioms, separation axioms, compactness, and connectedness. It also helps to understand the significance of various topological properties in classifying topological spaces.
This textbook focuses on general topology. Meant for graduate and senior undergraduate mathematics students, it introduces topology thoroughly from scratch and assumes minimal basic knowledge of real analysis and metric spaces. It begins with thought-provoking questions to encourage students to learn about topology and how it is related to, yet different from, geometry. Using concepts from real analysis and metric spaces, the definition of topology is introduced along with its motivation and importance. The text covers all the topics of topology, including homeomorphism, subspace topology, weak topology, product topology, quotient topology, coproduct topology, order topology, metric topology, and topological properties such as countability axioms, separation axioms, compactness, and connectedness. It also helps to understand the significance of various topological properties in classifying topological spaces.
Dr Jay Mehta is Assistant Professor in Department of Mathematics at Sardar Patel University, Gujarat, India. He is Ph.D. in Mathematics from Harish-Chandra Research Institute (HRI), Allahabad. His research interests include number theory and cryptography.
1. Preliminaries; 2. Topological Spaces 3. Continuous Functions; 4. Techniques of Creating Topologies: New from Old; 5. The Topology of Metric Spaces; 6. Countability Axioms; 7. Separation Axioms; 8. Compactness; 9. Connectedness; Appendix: From General Topology to Algebraic Topology; References; Index.
| Erscheint lt. Verlag | 28.2.2025 |
|---|---|
| Zusatzinfo | Worked examples or Exercises |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| ISBN-10 | 1-009-50588-2 / 1009505882 |
| ISBN-13 | 978-1-009-50588-8 / 9781009505888 |
| Zustand | Neuware |
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