1. The problem statement, all variables and given/known data http://img527.imageshack.us/img527/6049/48193240ao5.png [Broken] I don't understand this proof. The first two lines are clear to me: the sequence xn is in F and F is closed so its complement is open so there is a ball with radius r around x in Fc. But I don't understand the last two lines. Of course there y larger then the radius od the ball but what's the relation with the converging sequence?