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Function example? Continuous everywhere, differentiable nowhere

Is there any function that continuous in all places and not differentiable in all places?

do you know a good book about this?

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Mj125
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  • I added the reference-request tag as you ask for a book. – Hagen von Eitzen Dec 01 '12 at 17:59
  • Nice additional information: A randomly chosen continuous function is nearly "always" not differentiable in all places. For example the continous functions on $\left[0,1\right]$ that are not differentiable in all places are dense in all continous function on $\left[0,1\right]$ – user127.0.0.1 Dec 01 '12 at 18:15

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You could take a look at the Weierstrass function. There you can also find a list of references. "Counterexamples in analysis" of Gelbaum and Olmstead sounds very promising.

Hans Giebenrath
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