Exercise 12, § 8

Deduce from Exercise 11 that: a) If $A$ is a compact subset of $\mathbf{R}$, there is a continuous mapping of Cantor’s triadic set $K$ onto $A$ [take the $A(s)$ to be the intersections of $A$ with suitably chosen intervals]. b) If also $A$ is perfect and totally disconnected, it is homeomorphic to $K$ [same method, by arranging that if $s_1$ and $s_2$ are two distinct sequences with the same number of terms (equal to 0 or 1) then

]