Is the infinite (countable or uncountable) union of disjoint closed sets closed?
I think infinite (countable or uncountable) union of disjoint closed singleton sets should be open because if there are the union of infinitely many disjoint singletons, then we have the real numbers which is an open set.
What about the case of non-singleton uncountable disjoint union?
I don't known about the countable union of disjoint closed sets.