Invitation to Combinatorial Topology (eBook)

ForewordTranslator's PrefaceCHAPTER ONE. TOPOLOGICAL GENERALITIES1. Qualitative Geometric Properties2. Coloring Geographical Maps3. The Problem of Neighboring Regions4. "Topology, India-Rubber Geometry"5. Homeomorphism6. "Topology, Continuous Geometry"7. "Comparison of Elementary Geometry, Projective Geometry, and Topology"8. Relative Topological Properties9. Set Topology and Combinatorial Topology10. The Development of TopologyCHAPTER TWO. TOPOLOGICAL NOTIONS ABOUT SURFACES11. Descartes' Theorem12. An Application of Descartes' Theorem13. Characteristic of a Surface14. Unilateral Surfaces15. Orientability and Nonorientability16. Topological Polygons17. Construction of Closed Orientable Surfaces from Polygons by Identifying Their Sides18. Construction of Closed Nonorientable Surfaces from Polygons by Identifying Their Sides19. Topological Definition of a Closed SurfaceCHAPTER THREE. TOPOLOGICAL CLASSIFICATION OF CLOSED SURFACES20. The Principle Problem in the Topology of Surfaces21. Planar Polygonal Schema and Symbolic Representation of a Polyhedron22. Elementary Operations23. Use of Normal Forms of Polyhedra24. Reduction to Normal Form: I25. Reduction to Normal Form: II26. Characteristic and Orientability27. The Principle Theorem of the Topology of Closed Surfaces28. Application to the Geometric Theory of Functions29. Genus and Connection Number of Closed Orientable SurfacesBibliographyTRANSLATOR'S NOTESIndex