I am working on this problem, but I am stuck in the middle. Could someone please give me a hand?

I am trying to prove that the set of real numbers with topology on consisting of all sets of the form , where , is not a space.

I have is open in this space. So, is closed in this space and . Suppose there exist open in such that and . I claimed that . I don't see how an open set in can contain but does not contain because any open set in must be of the form . However, I don't have a rigorous argument here.