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?
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
Surprises and Counterexamples in Real Function Theory
Examples and Counterexamples in Graph Theory
Counter-Examples In Differential Equations And Related Topics