Elementary Topology Problem Textbook 1st Edition by Viro, Ivanov, Netsvetaev, Kharlamov ISBN 978-0821845066 0821845063
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Elementary Topology Problem Textbook 1st Edition by O.Ya. Viro, O.A. Ivanov, N.Yu. Netsvetaev, V.M. Kharlamov- Ebook PDF Instant Download/Delivery: 978-0821845066, 0821845063
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Product details:
ISBN 10: 0821845063
ISBN 13: 978-0821845066
Author: O.Ya. Viro, O.A. Ivanov, N.Yu. Netsvetaev, V.M. Kharlamov
This textbook on elementary topology contains a detailed introduction to general topology and an introduction to algebraic topology via its most classical and elementary segment centered at the notions of fundamental group and covering space. The book is tailored for the reader who is determined to work actively. The proofs of theorems are separated from their formulations and are gathered at the end of each chapter. This makes the book look like a pure problem book and encourages the reader to think through each formulation. A reader who prefers a more traditional style can either find the proofs at the end of the chapter or skip them altogether. This style also caters to the expert who needs a handbook and prefers formulations not overshadowed by proofs. Most of the proofs are simple and easy to discover. The book can be useful and enjoyable for readers with quite different backgrounds and interests. The text is structured in such a way that it is easy to determine what to expect from each piece and how to use it. There is core material, which makes up a relatively small part of the book. The core material is interspersed with examples, illustrative and training problems, and relevant discussions. The reader who has mastered the core material acquires a strong background in elementary topology and will feel at home in the environment of abstract mathematics. With almost no prerequisites (except real numbers), the book can serve as a text for a course on general and beginning algebraic topology.
Table of contents:
Part 1. General Topology
Chapter I. Structures and Spaces
1. Set-Theoretic Digression: Sets
2. Topology on a Set
3. Bases
4. Metric Spaces
5. Subspaces
6. Position of a Point with Respect to a Set
7. Ordered Sets
8. Cyclic Orders
Proofs and Comments
Chapter II. Continuity
9. Set-Theoretic Digression: Maps
10. Continuous Maps
11. Homeomorphisms
Proofs and Comments
Chapter III. Topological Properties
12. Connectedness
13. Application of Connectedness
14. Path Connectedness
15. Separation Axioms
16. Countability Axioms
17. Compactness
18. Sequential Compactness
19x. Local Compactness and Paracompactness
Proofs and Comments
Chapter IV. Topological Constructions
20. Multiplication
21. Quotient Spaces
22. Zoo of Quotient Spaces
23. Projective Spaces
24x. Finite Topological Spaces
25x. Spaces of Continuous Maps
Proofs and Comments
Chapter V. Topological Algebra
26x. Generalities on Groups
27x. Topological Groups
28x. Constructions
29x. Actions of Topological Groups
Proofs and Comments
Part 2. Elements of Algebraic Topology
Chapter VI. Fundamental Group
30. Homotopy
31. Homotopy Properties of Path Multiplication
32. Fundamental Group
33. The Role of Base Point
Proofs and Comments
Chapter VII. Covering Spaces and Calculation of Fundamental Groups
34. Covering Spaces
35. Theorems on Path Lifting
36. Calculation of Fundamental Groups by Using Universal Coverings
Proofs and Comments
Chapter VIII. Fundamental Group and Maps
37. Induced Homomorphisms and Their First Applications
38. Retractions and Fixed Points
39. Homotopy Equivalences
40. Covering Spaces via Fundamental Groups
41x. Classification of Covering Spaces
Proofs and Comments
Chapter IX. Cellular Techniques
42. Cellular Spaces
43x. Topological Properties of Cellular Spaces
44. Cellular Constructions
45. One-Dimensional Cellular Spaces
46. Fundamental Group of a Cellular Space
Proofs and Comments
Hints, Comments, Advices, Solutions, and Answers
Bibliography
Index
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Tags: Viro, Ivanov, Netsvetaev, Kharlamov, Elementary Topology, Problem Textbook