http://www.scribd.com/mobile/doc/76236535
page 49-50 Exercise 3.19
Let $A=\{0,2\}$ and $C$ be the Cantor Set. Define $x(\alpha) = \sum_{n=1}^\infty (\alpha_n / {3^n})$ for all $\alpha \in A^{\mathbb{N}}$.
Then $x$ is a well defined function.
I think the argument in the link assumed, without any notice, the existence of a sequence $\beta$ such that $x(\beta) = z$, for each $z\in C$.
Am I correct? Hence, the argument proves only ${ran} x \subset C$.
How do i prove that there exists a such sequence for each $z\in C$?