I have been able to find several counterexample books in some math areas. For example:

$\bullet$ Counterexamples in Analysis, Bernard R. Gelbaum, John M. H. Olmsted

$\bullet$ Counterexamples in Topology, Lynn Arthur Steen, J. Arthur Seebach Jr.

$\bullet$ Counterexamples in Probability and Statistics, Joseph P. Romano, A.F. Siegel

$\bullet$ Counterexamples in Probability and Real Analysis, Gary L. Wise and Eric B. Hall

$\bullet$ Counterexamples in Probability, Jordan M. Stoyanov

Why are there no other examples of books in other math topics (number theory, numerical analysis, DEQs, PDEs, Dynamical Systems, Discrete Math...)?

Is it that it is just not a rich enough area, examples are too trivial, the book wouldn't warrant publishing (low sales), someone just hasn't written one, I missed it or something else?


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    $\begingroup$ Your list is not complete. $\endgroup$ – Michael Greinecker Jan 15 '13 at 16:16
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    $\begingroup$ Nice question! Maybe, community wiki fits it? $\endgroup$ – Ilya Jan 15 '13 at 16:16
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    $\begingroup$ Great idea...I wish we'd have the opportunity to collect lists, even if Community Wiki, that people can update, modify, add...for many topics! +1 $\endgroup$ – Namaste May 21 '13 at 0:14
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    $\begingroup$ nice question !!! $\endgroup$ – user111750 Mar 11 '15 at 6:44

The following list of titles, all of which can be found on Amazon, may help to answer the question:

  • Counterexamples in Optimal Control Theory

  • Lectures on Counterexamples in Several Complex Variables

  • Counterexamples in Topological Vector Spaces

  • Theorems and Counterexamples in Mathematics

  • Counterexamples in Calculus

  • Convex Functions: Constructions, Characterizations and Counterexamples

  • Surprises and Counterexamples in Real Function Theory

  • Examples and Counterexamples in Graph Theory

  • Counter-Examples In Differential Equations And Related Topics

  • $\begingroup$ @michealGreinecker these books are very much addictive. It is a different kind of fun to read them. Please add a few more $\endgroup$ – Kislay Tripathi Oct 15 '17 at 11:56
  • Steen, L. A.; Seebach, J. A. jun., Counterexamples in topology, New York etc.: Holt, Rinehart and Winston, Inc., XIII, 210 p. (1970). ZBL0211.54401.

  • Gelbaum, B. R.; Olmsted, J. M. H., Counterexamples in analysis, Moskau: Verlag ’Mir’ 251 S. (1967). ZBL0156.05801.

  • Stoyanov, Jordan M., Counterexamples in probability, Wiley Series in Probability and Mathematical Statistics. Chichester etc.: John Wiley & Sons. XXIII, 313 p.; \textsterling 38.50 (1987). ZBL0629.60001.

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    $\begingroup$ All three of these books are mentioned in the original question... $\endgroup$ – Xander Henderson Sep 17 at 14:58
  • $\begingroup$ thanks. I followed a link directing me to the answer by Michael above directly so I overlooked the original post. $\endgroup$ – ALife Sep 18 at 14:35

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