Book:Lynn Arthur Steen/Counterexamples in Topology/Second Edition
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Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd Edition)
Published $\text {1978}$, Dover Publications, Inc.
- ISBN 0-486-68735-X
Subject Matter
Contents
- Preface
- Preface to the Second Edition
- PART I BASIC DEFINITIONS
- 1. General Introduction
- 3. Compactness
- Global Compactness Properties
- Localized Compactness Properties
- Countability Axioms and Separability
- Paracompactness
- Compactness Properties and $T_i$ Axioms
- Invariance Properties
- 3. Compactness
- 4. Connectedness
- Functions and Products
- Disconnectedness
- Biconnectedness and Continua
- 4. Connectedness
- PART II: COUNTEREXAMPLES
- 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. Fréchet Space
- 38. Hilbert Cube
- 39. Order Topology
- 40. Open Ordinal Space $\left[{\,0, \Gamma}\right)$ $\paren {\Gamma < \Omega}$
- 41. Closed Ordinal Space $\sqbrk {\,0, \Gamma}$ $\paren {\Gamma < \Omega}$
- 42. Open Ordinal Space $\left[{\,0, \Omega}\right)$
- 43. Closed Ordinal Space $\sqbrk {\,0, \Omega}$
- 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. Dieudonné 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. $\left[{\,0, \Omega}\right) \times I^I$
- 107. Helly Space
- 108. $C \sqbrk {0, 1}$
- 109. Box Product Topology on $R^\omega$
- 110. Stone-Čech Compactification
- 111. Stone-Čech 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 Angles
- 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
- PART III: METRIZATION THEORY
- Conjectures and Counterexamples
- PART IV: APPENDICES
- Special Reference Charts
- Separation Axiom Chart
- Compactness Chart
- Paracompactness Chart
- Connectedness Chart
- Disconnectedness Chart
- Metrizability Chart
- General Reference Chart
- Problems
- Notes
- Bibliography
- Special Reference Charts
- Index
Further Editions
Click here for errata
Source work progress
- 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text {II}$: Counterexamples: $42$. Open Ordinal Space $[0, \Omega)$: $10$