pagetitle	author
A solutions manual for Topology by James Munkres	https://github.com/9beach

A solutions manual for Topology by James Munkres

GitHub repository here, HTML versions here, and PDF version here.

Contents

Chapter 1. Set Theory and Logic

1. Fundamental Concepts
2. Functions
3. Relations
4. The Integers and the Real Numbers
5. Cartesian Products
6. Finite Sets
7. Countable and Uncountable Sets
8. The Principle of Recursive Definition
9. Infinite Sets and the Axiom of Choice
10. Well-Ordered Sets
11. The Maximum Principle

Chapter 2. Topological Spaces and Continuous Functions

12. Topological Spaces
13. Basis for a Topology
14. The Order Topology
15. The Product Topology on X × Y
16. The Subspace Topology
17. Closed Sets and Limit Point
18. Continuous Functions
19. The Product Topology
20. The Metric Topology
21. The Metric Topology (continued)
22. The Quotient Topology

Chapter 3. Connectedness and Compactness

23. Connected Spaces
24. Connected Subspaces of the Real Line
25. Components and Local Connectedness
26. Compact Spaces
27. Compact Subspaces of the Real Line
28. Limit Point Compactness
29. Local Compactness

Chapter 4. Countability and Separation Axioms

30. The Countability Axioms
31. The Separation Axioms
32. Normal Spaces
33. The Urysohn Lemma
34. The Urysohn Metrization Theorem
35. The Tietze Extension Theorem
36. Imbeddings of Manifolds

Chapter 5. The Tychonoff Theorem

37. The Tychonoff Theorem
38. The Stone-Čech Compactification

Chapter 6. Metrization Theorems and Paracompactness

39. Local Finiteness
40. The Nagata-Smirnov Metrization Theorem
41. Paracompactness
42. The Smirnov Metrization Theorem

Chapter 7. Complete Metric Spaces and Function Spaces

43. Complete Metric Spaces
44. A Space-Filling Curve
45. Compactness in Metric Spaces
46. Pointwise and Compact Convergence
47. Ascoli’s Theorem

Chapter 8. Baire Spaces and Dimension Theory

48. Baire Spaces
49. A Nowhere-Differentiable Function
50. Introduction to Dimension Theory

Chapter 9. The Fundamental Group

51. Homotopy of Paths
52. The Fundamental Group
53. Covering Spaces
54. The Fundamental Group of the Circle
55. Retractions and Fixed Points
56. The Fundamental Theorem of Algebra
57. The Borsuk-Ulam Theorem
58. Deformation Retracts and Homotopy Type
59. The Fundamental Group of Sn
60. Fundamental Groups of Some Surfaces

Chapter 10. Separation Theorems in the Plane

61. The Jordan Separation Theorem
62. Invariance of Domain
63. The Jordan Curve Theorem
64. Imbedding Graphs in the Plane
65. The Winding Number of a Simple Closed Curve
66. The Cauchy Integral Formula

Chapter 11. The Seifert-van Kampen Theorem

67. Direct Sums of Abelian Groups
68. Free Products of Groups
69. Free Groups
70. The Seifert-van Kampen Theorem
71. The Fundamental Group of a Wedge of Circles
72. Adjoining a Two-cell
73. The Fundamental Groups of the Torus and the Dunce Cap

Chapter 12. Classification of Surfaces

74. Fundamental Groups of Surfaces
75. Homology of Surfaces
76. Cutting and Pasting
77. The Classification Theorem
78. Constructing Compact Surfaces

Chapter 13. Classification of Covering Spaces

79. Equivalence of Covering Spaces
80. The Universal Covering Space
81. Covering Transformations
82. Existence of Covering Spaces