I'm studying the topology in $\mathbb{R}$ of open and closed intervals, and
I have some doubts regarding why I can have a topology of open intervals (in which I can have the generalized union but only the intersection of a finite number of sets) but not a topology of closed intervals (in which I can have the generalized intersection but only the union of a finite number of sets)
I think this as a natural fact considering that an interval is open if the complementary set is closed and vice versa.
Can someone help me to understand why? it is a convenction or is there a reason?