Exercise 2, § 1

There exists a continuous mapping of the interval $I - [0, 1]$ of $\mathbf{R}$ onto the square $I \times I$ of $\mathbf{R}^2$ (the “Peano curve”, cf. Exercise 8). Show first, with the help of Exercise 11 of Chapter IV, § 8, that there exists a continuous mapping $f$ of Cantor’s triadic set $K$ onto $I / I$, and then extend $f$ to $I$.