Proof problem Let (P. 5) be a post. We will call a subset U C P( P) an open subset of P If and only if the following holds: Il peU and p s q, then q E U. In other words, O C P is open if and only if it is "upward closed." Example 0.0.3. The empty art O C P Is open. The entire set P is open. Here is the problem: () Let U : 4 - 3(P) be a function such that, for every o E A, U. is an open subect of P. Show that UU. is open. (In words: You are showing that the union of opera subacts is open.)\f