Book:E.M. Patterson/Topology/Second Edition

Subject Matter

 * Topology

Contents

 * Preface
 * Preface to the Second Edition


 * $\text {I}$ INTRODUCTION


 * 1. Topological Equivalence
 * 2. Surfaces
 * 3. Two sidedness and Orientability
 * 4. Connection
 * 5. Topological Invariants
 * 6. Euler's Theorem on polyhedra
 * 7. The colouring of maps


 * $\text {II}$ TOPOLOGICAL SPACES


 * 8. Notations and definitions of set theory
 * 9. Functions
 * 10. Equivalence relations
 * 11. Continuity on the Euclidean line
 * 12. Continuity in the Euclidean plane
 * 13. Euclidean space of $n$ dimensions
 * 14. Metric spaces
 * 15. Continuity in metric spaces
 * 16. Open sets and related concepts in metric spaces
 * 17. Theorems on metric spaces
 * 18. Topological spaces
 * 19. Some theorems on topological spaces
 * 20. Alternative methods of defining a topological space
 * 21. Bases
 * 22. Relative topology
 * 23. Identification
 * 24. Topological products
 * 25. Topological groups


 * $\text {III}$ PARTICULAR TYPES OF TOPOLOGICAL SPACES


 * 26. Hausdorff spaces
 * 27. Normal spaces
 * 28. Convergence
 * 29. Compactness
 * 30. Connectedness


 * $\text {VI}$ HOMOTOPY


 * 31. Introduction
 * 32. Theorems on homotopy
 * 33. Homotopy type
 * 34. Paths
 * 35. The fundamental group
 * 36. The Homotopy Groups


 * $\text {V}$ SIMPLICIAL COMPLEXES


 * 37. Introduction
 * 38. Linear subspaces of Euclidean space
 * 39. Simplexes
 * 40. Orientation of simplexes
 * 41. Simplical complexes
 * 42. Incidence
 * 43. Triangulation
 * 44. Examples of Triangulation


 * $\text {VI}$ HOMOLOGY


 * 45. Introduciton
 * 46. Finitely generated Abelian groups
 * 47. Chains
 * 48. Boundaries
 * 49. Cycles
 * 50. Homology Groups
 * 51. Betti numbers
 * 52. Chains over an arbitrary Abelian group
 * 53. Cohomology
 * 54. Calculation of homology groups





Source work progress
* : Chapter $\text {II}$: Topological Spaces: $\S 11$. Continuity on the Euclidean line