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Counterexamples in Topology
by Lynn Arthur Steen and J. Arthur Seebach, Jr.

[Our review of this book]


  1. General Introduction
    Limit Points
    Closures and Interiors
    Countability Properties
  2. Separation Axioms
    Regular and Normal Spaces
    Completely Hausdorff Spaces
    Completely Regular Spaces
    Functions, Products, and Subspaces
    Additional Separation Properties
  3. Compactness
    Global Compactness Properties
    Localized Compactness Properties
    Countability Axioms and Separability
    Compactness Properties and T_i Axioms
    Invariance Properties
  4. Connected
    Functions and Products
    Biconnectedness and Continua
  5. Metric Spaces
    Complete Metric Spaces
    Metric Uniformities


  1. Finite Discrete Topology
  2. Countable Discrete Topology
  3. Uncountable Discrete Topology
  4. Indiscrete Topology
  5. Partition Topology
  6. Odd-Even Topology
  7. Deleted Integer Topology
  8. Finite Particular Point Topology
  9. Countable Particular Point Topology
  10. Uncountable Particular Point Topology
  11. Sierpinski Space
  12. Closed Extension Topology
  13. Finite Excluded Point Topology
  14. Countable Excluded Point Topology
  15. Uncountable Excluded Point Topology
  16. Open Extension Topology
  17. Either-Or Topology
  18. Finite Complement Topology on a Countable Space
  19. Finite Complement Topology on an Uncountable Space
  20. Countable Complement Topology
  21. Double Pointed Countable Complement Topology
  22. Compact Complement Topology
  23. Countable Fort Space
  24. Uncountable Fort Space
  25. Fortissimo Space
  26. Arens-Fort Space
  27. Modified Fort Space
  28. Euclidean Topology
  29. The Cantor Set
  30. The Rational Numbers
  31. The Irrational Numbers
  32. Special Subsets of the Real Line
  33. Special Subsets of the Plane
  34. One Point Compactification Topology
  35. One Point Compactification of the Rationals
  36. Hilbert Space
  37. Frechet Space
  38. Hilbert Cube
  39. Order Topology
  40. Open Ordinal Space [0,Gamma) (Gamma < Omega)
  41. Closed Ordinal Space [0,Gamma] (Gamma < Omega)
  42. Open Ordinal Space [0,Omega)
  43. Closed Ordinal Space [0,Omega]
  44. Uncountable Discrete Ordinal Space
  45. The Long Line
  46. The Extended Long Line
  47. An Altered Long Line
  48. Lexicographic Ordering on the Unit Square
  49. Right Order Topology
  50. Right Order Topology on R
  51. Right Half-Open Interval Topology
  52. Nested Interval Topology
  53. Overlapping Interval Topology
  54. Interlocking Interval Topology
  55. Hjalmar Ekdal Topology
  56. Prime Ideal Topology
  57. Divisor Topology
  58. Evenly Spaced Integer Topology
  59. The p-adic Topology on Z
  60. Relatively Prime Integer Topology
  61. Prime Integer Topology
  62. Double Pointed Reals
  63. Countable Complement Extension Topology
  64. Smirnov's Deleted Sequence Topology
  65. Rational Sequence Topology
  66. Indiscrete Rational Extension of R
  67. Indiscrete Irrational Extension of R
  68. Pointed Rational Extension of R
  69. Pointed Irrational Extension of R
  70. Discrete Rational Extension of R
  71. Discrete Irrational Extension of R
  72. Rational Extension in the Plane
  73. Telophase Topology
  74. Double Origin Topology
  75. Irrational Slope Topology
  76. Deleted Diameter Topology
  77. Deleted Radius Topology
  78. Half-Disc Topology
  79. Irregular Lattice Topology
  80. Arens Square
  81. Simplified Arens Square
  82. Niemytzki's Tangent Disc Topology
  83. Metrizable Tangent Disc Topology
  84. Sorgenfrey's Half-Open Square Topology
  85. Michael's Product Topology
  86. Tychonoff Plank
  87. Deleted Tychonoff Plank
  88. Alexandroff Plank
  89. Dieudonne Plank
  90. Tychonoff Corkscrew
  91. Deleted Tychonoff Corkscrew
  92. Hewitt's Condensed Corkscrew
  93. Thomas' Plank
  94. Thomas' Corkscrew
  95. Weak Parallel Line Topology
  96. Strong Parallel Line Topology
  97. Concentric Circles
  98. Appert Space
  99. Maximal Compact Topology
  100. Minimal Hausdorff Topology
  101. Alexandroff Square
  102. Z^Z
  103. Uncountable Products of Z+
  104. Baire Product Metric on R^omega
  105. I^I
  106. [0,Omega) X I^I
  107. Helly Space
  108. C[0,1]
  109. Box Product Topology on R^omega
  110. Stone-Cech Compactification
  111. Stone-Cech Compactification of the Integers
  112. Novak Space
  113. Strong Ultrafilter Topology
  114. Single Ultrafilter Topology
  115. Nested Rectangles
  116. Topologist's Sine Curve
  117. Closed Topologist's Sine Curve
  118. Extended Topologist's Sine Curve
  119. The Infinite Broom
  120. The Closed Infinite Broom
  121. The Integer Broom
  122. Nested Angels
  123. The Infinite Cage
  124. Bernstein's Connected Sets
  125. Gustin's Sequence Space
  126. Roy's Lattice Space
  127. Roy's Lattice Subspace
  128. Cantor's Leaky Tent
  129. Cantor's Teepee
  130. A Pseudo-Arc
  131. Miller's Biconnected Set
  132. Wheel without Its Hub
  133. Tangora's Connected Space
  134. Bounded Metrics
  135. Sierpinski's Metric Space
  136. Duncan's Space
  137. Cauchy Completion
  138. Hausdorff's Metric Topology
  139. The Post Office Metric
  140. The Radial Metric
  141. Radial Interval Topology
  142. Bing's Discrete Extension Space
  143. Michael's Closed Subspace




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