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Invitation to Combinatorial Topology by Maurice Fréchet,Ky Fan,Howard W. Eves ISBN: 0486427862 Dover Publications Price: $9.95 click here to see this book An elementary text that can be understood by anyone with a background in high school geometry, this text focuses on the problems inherent to coloring maps, homeomorphism, applications of Descartes' theorem, and topological polygons. Considerations of the topological classification of closed surfaces cover elementary operations, use of normal forms of polyhedra, more. Includes 108 figures. 1967 edition. Unabridged republication of Initiation to Combinatorial Topology, published by Prindle, Weber & Schmidt, Inc., Boston, 1967. Table of Contents for Invitation to Combinatorial Topology Foreword Translator's Preface CHAPTER ONE. TOPOLOGICAL GENERALITIES 1. Qualitative Geometric Properties 2. Coloring Geographical Maps 3. The Problem of Neighboring Regions 4. "Topology, India-Rubber Geometry" 5. Homeomorphism 6. "Topology, Continuous Geometry" 7. "Comparison of Elementary Geometry, Projective Geometry, and Topology" 8. Relative Topological Properties 9. Set Topology and Combinatorial Topology 10. The Development of Topology CHAPTER TWO. TOPOLOGICAL NOTIONS ABOUT SURFACES 11. Descartes' Theorem 12. An Application of Descartes' Theorem 13. Characteristic of a Surface 14. Unilateral Surfaces 15. Orientability and Nonorientability 16. Topological Polygons 17. Construction of Closed Orientable Surfaces from Polygons by Identifying Their Sides 18. Construction of Closed Nonorientable Surfaces from Polygons by Identifying Their Sides 19. Topological Definition of a Closed Surface CHAPTER THREE. TOPOLOGICAL CLASSIFICATION OF CLOSED SURFACES 20. The Principle Problem in the Topology of Surfaces 21. Planar Polygonal Schema and Symbolic Representation of a Polyhedron 22. Elementary Operations 23. Use of Normal Forms of Polyhedra 24. Reduction to Normal Form: I 25. Reduction to Normal Form: II 26. Characteristic and Orientability 27. The Principle Theorem of the Topology of Closed Surfaces 28. Application to the Geometric Theory of Functions 29. Genus and Connection Number of Closed Orientable Surfaces Bibliography TRANSLATOR'S NOTES Index

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