a) Pick an , what is the ball of radius 1/2 around x?
b) Apply a) to the complement of Y
Let X be set donoted by the discrete metrics
d(x; y) =(0 if x = y;
1 if x not equal y:
(a) Show that any sub set Y of X is open in X
(b) Show that any sub set Y of X is closed in X
so what would be the steps to ans this question?
As I tried to form an answer with the union of balls B(x,r), as in Y of X we have Y= Union (Y) is open for y in Y....ie union of open sets is open therefore y is open.
Then for b) I tried let Y be a subset of X, the X\Y is open and Y is closed....but i need to explain more....please help !