1. Show that the intervals (-?, a] and [a, ?), Va ? R, are closed subsets of R.
2. (a) Let A ? R be closed and let {an} be a sequence in A which converges to a ? R.
Show that a ? A.
(b) Show by example that the conclusion in (a) is false if A is not closed.
3. Let A ? R be bounded, and let ? = sup A, ? = inf A. Show that ?, ? ? A.
4. Suppose A ? R is a finite set, namely, A = {a1, a2,…, an}, ai ? R, i = 1,..., n, for
some n ? N. Show that A is closed.