Does anyone know of a diagram that displays and organizes categories of functions according to their calculus-related properties (e.g. continuous, $C^\infty$, degrees of differentiability and integrability; not so much things like even/odd, one-to-one)? Something along the lines of what this diagram does for complex numbers.
[The original of this (and more) can be found here.]
I would be grateful if you could direct me to any good resources that categorize types of functions in a systematic and succinct manner. Illuminating examples of the different types of functions (e.g. Weierstrass's continuous-everywhere-but-differentiable-nowhere function) and schematic clarity would be pluses.
Let me know if you need more information. Thanks!
Edit: I've look around more on this site at related questions (notably Are the smooth functions dense in either L^2 or L^1? and what is the cardinality of set of all smooth functions in $L^1$?) and found them intriguing and somewhat helpful. I could really use help putting all of these and many other pieces together, though. Any takers?