Exercise 3.2.1

(a)

Where in the proof of Theorem 3.2.3 part (ii) does the assumption that the collection of open sets be finite get used?

(b)

Give an example of a countable collection of open sets $\left\{O_1,O_2,O_3,\dots \right\}$ whose intersection ${\bigcap <!--\; FUNCTION\; APPLICATION\; -->}_{n=1}^{\infty }{O}_n$ is closed, not empty and not all of $R$.