Recall our denitions of the interior 9, the closure Q and the boundary 69 of a set 9 C R as 9 U U, Q: n V, and an=\ . U open, UCQ V closed, QCV Now prove the following characterizations of open and closed sets: (a) Wehave: 69={mER: Vr>0z Vr(m)Q7E(Zl/\\ 14493090759}