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