# Fixed Points

### About this Title

**Yu. A. Shashkin**, *Institute for Mathematics and Mechanics, Ekaterinburg, Russia*

Publication: Mathematical World

Publication Year
1991: Volume 2

ISBNs: 978-0-8218-9000-4 (print); 978-1-4704-2470-1 (online)

DOI: http://dx.doi.org/10.1090/mawrld/002

MathSciNet review: MR1143284

MSC: Primary 55M20; Secondary 54-01, 54H25, 55-01

### Table of Contents

**Front/Back Matter**

**Chapters**

- Chapter 1. Continuous Mappings of a Closed Interval and a Square
- Chapter 2. First Combinatorial Lemma
- Chapter 3. Second Combinatorial Lemma, or Walks through the Rooms in a House
- Chapter 4. Sperner’s Lemma
- Chapter 5. Continuous Mappings, Homeomorphisms and the Fixed Point Property
- Chapter 6. Compactness
- Chapter 7. Proof of Brouwer’s Theorem for a Closed Interval, the Intermediate Value Theorem, and Applications
- Chapter 8. Proof of Brouwer’s Theorem for a Square
- Chapter 9. The Iteration Method
- Chapter 10. Retraction
- Chapter 11. Continuous Mappings of a Circle, Homotopy, and Degree of a Mapping
- Chapter 12. Second Definition of the Degree of a Mapping
- Chapter 13. Continuous Mappings of a Sphere
- Chapter 14. Theorem on Equality of Degrees
- Solutions and Answers