I realize I can use the complement of 5. to get 4. - I would, however, still appreciate a direct method if anyone knows.
As for 3., I might be going crazy .. intuitively, I think the statement is true. After all, since is continuous on , it is continuous on . If it were an interval l could look at , where and , I could use continuity to show that the function is bounded on the interval. But is a set - and I'm not sure how that changes things.