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

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E.M. Patterson: Topology (Second Edition)

Published $1959$, Oliver and Boyd Ltd.


Subject Matter


Contents

Preface
Preface to the Second Edition


Chapter 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 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 III Particular Types of Topological Spaces
26. Hausdorff spaces
27. Normal spaces
28. Convergence
29. Compactness
30. Connectedness


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


Chapter 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 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


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