On page 51 in Royden, the definition of Cantor-Lebesgue function $\emptyset$ on the cantor set is:$$\emptyset (x) = \sup\{\emptyset(t)| t \in O\cap[0, x)\}, \text{ if } x\in C\setminus\{0\}.$$
Where, for each $k$, let $O_{k}$ be the union of the $2^k -1$ intervals which have been removed during the first $k$ stages of the Cantor deletion process and $O = \cup_{k=1}^{\infty} O_{k}.$
My question is:
Can anyone give me a numerical example for this definition, please?