Sorry, is this the right forum for this type of question? This is from my analysis class. Thanks.
(1)
Let
(a) Find the limit points of .
(b) Is a closed set?
(c) Is an open set?
(d) Does contain any isolated points?
(e) Find
(For (e), use this definition. Given a set A , let L be the set of all limit points of A. The closure of A is defined to be = A L
(2) Decide wheather the following sets are open, closed, or neither. If a set is not open, find a point in the set for which there is no -neighborhood contained in the set. If a set is not closed, find a limit point that is not contained in the set.
(a) -rational numbers
(b) -natural numbers
(c)
(d) (0,1]=
(e) {1+1/4+1/9+...+1/ }
(3) Let Prove that is an isolated point of A if and only if there exists an -neighborhood such that A= .
Any and all help would be greatly appreciated, thanks!