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.
Good luck.
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.