For (a) consider the family of open sets
What happens when you take the intersection of
This should get you started on (a) and (b)
Also remember that in points are closed and is a countable set.
A set is called an set if it can be written as the countable union of closed sets. A set is called a set if it can be written as the countable intersection of open sets.
(a) Show that a closed interval [a, b] is a set.
(b) Show that the half open interval (a, b] is both a and an set.
(c) Show that is an set, and the set of irrationals forms a set.
I have no idea where to start on this problem. Any help would be appreciated. Thank you for your time.