Let X be a set donated by the discrete metrics
d(x,y) = 0 if x=y,
1 if x̸=y.
Show that a subset Y of X is compact iff this set is closed
First, notice converges iff it becomes constant after a certain . With that, every subset is closed.
Now, im not sure about this excercise. I think must be finite... if not we may choose , and the sequence that doesn't have any convergent sub-sequence 'cause it never become constant.