Jiri Lebl. "Cantor function" (version 6). PlanetMath.org. Freely available at http://planetmath.org/CantorFunction.html.

AMS MSC:

26A30 (Real functions :: Functions of one variable :: Singular functions, Cantor functions, functions with other special properties)

NS:published, NS:Section:Reference

Devil's staircase by Andrew Archibald on 2004-04-06 21:01:49 A nice article on Cantor's function (the Devil's staircase) finishes with a tanatlizing comment: Such functions turn up in many areas of mathematics and are not just pathological examples. Nice to say that, but it really provokes the question: where do they turn up? The only example I can think of off-hand is of locally constant functions on $p$-adic fields, and that's a bit iffy: the base field is pretty different from $\mathbb{R}$. I suppose they provide a counterexample for the simplest interpretation of the Fundamental Theorem of Calculus, but that hardly helps them qualify as non-pathological. [ reply | up ]

Re: Devil's staircase by Boris Bukh on 2004-04-06 21:55:01 Re: Devil's staircase by Andrew Archibald on 2004-04-06 22:11:18 Re: Devil's staircase by Boris Bukh on 2004-04-06 22:38:11 Re: Devil's staircase by Jiri Lebl on 2004-04-11 21:06:57 Re: Devil's staircase by Andrew Archibald on 2004-04-12 05:38:24