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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.

Complex Number Venn Diagram

[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 $\mathcal L_2$ or $\mathcal L_1$? 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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    You might find this book somewhat helpful: http://books.google.com/books?id=cDAMh5n4lkkC&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false2011-08-16

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From the book A Second Course on Real Functions by van Rooij & Schikhof:

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The publisher allows you to read excerpts online: the introduction, where this figure is taken from, and the table of contents, including a four-page list of examples & counterexamples.

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    You're welcome! And here is, incidentally, [a similar diagram](http://www.ams.org/notices/200109/fea-saloff.pdf) (Fig 3) on a completely different topic.2015-01-23
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In your diagram: delete the Imaginary axis, change Integer to "Polynomial with a finite number of terms", change Rational to Rational function, change Algebraic to Algebraic function. I'm not sure what Real corresponds to. On another axis you could have the C^1>C^2 ... as you mentioned. On another axis you could have the field of the polynomial, i.e. "polynomial over integers", "polynomial over real", "polynomial over complex", "polynomial over vector space", etc.