Chapter 4.33, Problem 1E

Examine the proof of the Urysohn lemma, and show that for given $r$,

$f^{-1}\left(r\right)={\displaystyle \underset{p>r}{\cap }{U}_p}-{\displaystyle \underset{q<r}{\cup }{U}_q}$,

$p$, $q$ rational.