I've attempted to write an arbitrary subset of real numbers as the union of it's single points.
Any single point set is closed. But I don't know if the union of all single points of a subset of reals like A is closed or not? (suppose A is infinite) also i have this problem for writing A as the intersect of open subsets, because the intersection of an infinite number of open subsets may not be open. for example can we write [0,1) as the union of the sets [0, 1 - 1/n] for n in naturals, as the union of countable infinite closed sets?