I would like to ask whether there is a reference which collects pathological examples in mathematics (in general). What I mean is that, for instance, consider Weierstrass function. It has the property that it is continuous everywhere but differentiable nowhere. Similarly, Cantor set has uncountably many elements but its Lebesgue measure is zero.
I know that sets and functions are different concepts but the critical progresses are generally based on these pathological examples. I wonder if there are references that completely focus on these type of examples.
Also, I am sure that there are many interesting functions, sets or other objects that teach much about the related subjects. Other reference suggestions, which examine the subjects over these examples, in that sense are more than welcome.