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Intuitive Topology
V. V. Prasolov, Moscow, Russia

Mathematical World
1994; 93 pp; softcover
Volume: 4
Reprint/Revision History:
reprinted 1998
ISBN-10: 0-8218-0356-5
ISBN-13: 978-0-8218-0356-1
List Price: US$25
Member Price: US$20
Order Code: MAWRLD/4
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This book is an introduction to elementary topology presented in an intuitive way, emphasizing the visual aspect. Examples of nontrivial and often unexpected topological phenomena acquaint the reader with the picturesque world of knots, links, vector fields, and two-dimensional surfaces. The book begins with definitions presented in a tangible and perceptible way, on an everyday level, and progressively makes them more precise and rigorous, eventually reaching the level of fairly sophisticated proofs. This allows meaningful problems to be tackled from the outset. Another unusual trait of this book is that it deals mainly with constructions and maps, rather than with proofs that certain maps and constructions do or do not exist. The numerous illustrations are an essential feature. The book is accessible not only to undergraduates but also to high school students and will interest any reader who has some feeling for the visual elegance of geometry and topology.


Advanced high school students and undergraduates majoring in mathematics.


"The title is highly descriptive of the contents of this book. The reader is carried along, mostly through sketches in rubber sheet geometry, to an appreciation of some interesting knot and link theory ... In all, a most entertaining exposition."

-- Zentralblatt MATH

Table of Contents

  • Deformations
  • Knots and links
  • Spans of knots and links
  • A knot invariant
  • Homeomorphisms
  • Vector fields on the plane
  • Vector fields on two-dimensional surfaces
  • Fixed point free and periodic homeomorphisms
  • Two-dimensional surfaces
  • References
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