Elementary Topology Problem Textbook by O.Ya.Viro, et al.
Elementary Topology Problem Textbook - Table of Contents
PART I - GENERAL TOPOLOGY
1. Structures and Spaces
2. Continuity
3. Topological Properties
4. Topological Constructions
5. Topological Algebra
PART II - ALGEBRAIC TOPOLOGY
6. Fundamental Group
7. Covering Spaces and Calculation of Fundamental Groups
8. Fundamental Group and Maps
9. Cellular Techniques
PART III - TOPOLOGICAL MANIFOLDS
10. Manifolds
11. Classifications in Low Dimensions
12. Surfaces Beyond Classification
13. One-Dimensional Homology
What You Will Learn in Elementary Topology Problem Textbook
"Elementary Topology: Problem Textbook" by O.Ya. Viro, O.A. Ivanov, N.Yu. Netsvetaev, and V.M. Kharlamov is a "problem-based" introduction to "topology" that blends theory with active learning. It focuses on fundamental concepts such as "topological spaces", "continuity", "algebraic topology", and the "fundamental group", offering students a hands-on approach to understanding abstract structures through carefully designed exercises.
The book separates "theorems" from proofs, encouraging readers to think critically and explore why results hold rather than just memorizing statements. Topics covered include general topology, standard constructions, open and closed sets, metric spaces, compactness, connectedness, and the basic ideas of algebraic topology, including covering spaces. Each chapter combines clear explanations with illustrative problems, promoting intuition, problem-solving skills, and independent reasoning.
Ideal for both self-study and classroom use, this textbook is accessible to students with minimal prerequisites, requiring only familiarity with real numbers. Its problem-centered approach not only reinforces theoretical understanding but also strengthens analytical thinking, making abstract concepts concrete. By working through examples and exercises, learners gain confidence in tackling proofs, understanding "topological spaces", and applying key ideas in both general and algebraic topology.
Book Details & Specifications
Title:
Elementary Topology Problem Textbook by O.Ya.Viro, et al.
Publisher:
American Mathematical Society
Year:
2008
Pages:
415
Type:
PDF
Language:
English
ISBN-10 #:
0821845063
ISBN-13 #:
978-0821845066
License:
External Educational Resource
Amazon:
Amazon
About the Author: O.Ya.Viro
The author O.Ya.Viro
is a renowned "Russian mathematician" known for his contributions to "topology" and algebraic geometry. He has developed influential methods such as "patchworking" and held positions at institutions including "Stony Brook University" and the Steklov Institute of Mathematics, connecting deep theoretical ideas with geometric intuition. He is the lead author of "Elementary Topology: Problem Textbook", co-written with O.?A.?Ivanov, N.?Yu.?Netsvetaev, and V.?M.?Kharlamov. The book teaches "general topology" and "algebraic topology" through a problem-based approach, covering metric spaces, continuity, and the fundamental group.
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