Book:E.M. Patterson/Topology/Second Edition
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E.M. Patterson: Topology (Second Edition)
Published $\text {1959}$, Oliver and Boyd Ltd
Subject Matter
Contents
- Preface
- Preface to the Second Edition
- chapter $\text {I}$ 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
- chapter $\text {II}$ 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
- chapter $\text {III}$ PARTICULAR TYPES OF TOPOLOGICAL SPACES
- 26. Hausdorff spaces
- 27. Normal spaces
- 28. Convergence
- 29. Compactness
- 30. Connectedness
- chapter $\text {VI}$ HOMOTOPY
- 31. Introduction
- 32. Theorems on homotopy
- 33. Homotopy type
- 34. Paths
- 35. The fundamental group
- 36. The Homotopy Groups
- chapter $\text {V}$ 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
- chapter $\text {VI}$ 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
- Bibliography
- Index
Further Editions
- 1956: E.M. Patterson: Topology
Source work progress
- 1959: E.M. Patterson: Topology (2nd ed.) ... (previous) ... (next): Chapter $\text {II}$: Topological Spaces: $\S 11$. Continuity on the Euclidean line