Counterexamples in Topology
Counterexamples in Topology is a book by topologists Lynn A. Steen and J. Arthur Seebach, Jr. who, together with their graduate students, canvassed the field of topology for a wide grouping of topological counterexamples. If you're wondering whether one property of topological spaces follows from another, this book can usually provide a counterexample if it's false. For example, is there an example of a first-countable space which is not second-countable? Several other "Counterexamples in ..." books and papers have followed.
Note that several of the naming conventions in this book differ from those in BambooWeb, particularly with respect to the separation axioms. Steen and Seebach exchange the meanings of T3, T4, and T5 with those of regular, normal, and completely normal. They also exchange the meanings of completely Hausdorff with Finite discrete topology
- 2. Countable discrete topology
- 3. Uncountable discrete topology
- 4. Indiscrete topology
- 11. Sierpinski space
- 18. Finite complement topology on a countable space
- 19. Finite complement topology on an uncountable space
- 20. Countable complement topology
- 28. Euclidean topology
- 29. Cantor set
- 30. Rational numbers
- 31. Irrational numbers
- 36. Hilbert space
- 37. Hilbert cube
- 39. Order topology
- 45. Long line
- 46. Extended long line
- 51. Right half-open interval topology
- 84. Sorgenfrey's half-open square topology
- 116. Topologist's sine curve
- 117. Closed topologist's sine curve
- 118. Extended topologist's sine curve
See also
References
- Lynn Arthur Steen and J. Arthur Seebach, Jr., Counterexamples in Topology. Springer-Verlag, New York, 1978. Reprinted by Dover Publications, New York, 1995. ISBN 0-486-68735-X (Dover edition).
