Difficult# Definition of Continuous Maps 2

TOPO-WNDPE9

Consider the function:

$$f(x)=\begin{cases} \frac{1}{n }\ \text{if }\ x=\frac{m}{n} \in \mathbb{Q}\ \ \text{(most reduced form)}\\\ 0\ \ \text{if }\ x \notin \mathbb{Q}\end{cases}$$

...on the interval $[0,1]$. Which one of the following statements is **TRUE**?