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Let C denote the Cantor set constructed by removing the typical open middle thirds inductively from the interval [0,1] in R.

I denote as f the characteristic function of C, i.e., f(x)=1 if x belongs to C and f(x)=0 otherwise.

I guess that the set of discontinuities of f is C (in the usual topology of R).

Could anyone show a proof of this or give a reference for one?

Many thanks!

Juan Reyes
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1 Answers1

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Hint: the Cantor set is a closed set with empty interior.

GaC
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