# Topology question?

by waht
Tags: topology
 P: n/a So for each x in A, there exists an open set U(x) such that $x \in U(x) \subseteq A$. Let O be the union of all such open sets, $O = \bigcup_{x \in A} U(x)$. Show that O is open, and that O = A. (Remember, the union of any collection of open sets is open, by definition).