# Organizing types of functions by their calculus-related properties, in diagram form?

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.

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?

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Is there really a nice hierarchy? Sure you could split functions up into analytic ones, meromorphic ones, those functions with branch cuts... and then genuine monsters, but what's the point of a hierarchy? –  Guess who it is. Aug 16 '11 at 4:37
I don't know if there's a hierarchy or interesting interactions of categories. I'm asking because I don't know this terrain very well and am hoping for a better and more unified understanding of the possibilities, intricacies, and surprises that exist. One thing I've thought of is how there's continuous>C^1>...>C^inf. I'm not sure what all else is going on. –  Justin Lanier Aug 16 '11 at 4:51
You might find this book somewhat helpful: books.google.com/… –  John M Aug 16 '11 at 10:09