Problem 9: For any x E E, define Ex = {y E Ely ~ x}, which is a subset of E of course. Show that we have the following disjoint partition of E: E =UEx. TEE That is, for x1, 12 E E, either Ex = Ex2 or Ex, n Ex2 = 0. Problem 10 (Continued from Problem 9): Show that each Ex may be represented in the form Ex = x + Qx, XEE, Q. CQ, and that if E is bounded so is Qx