Prove, that you can't "produce" $\mathbb{R}$ with countable amount of sets, which are nowhere dense(I am not sure I said this definition correct, with nowhere dense, I mean that $Int(\overline X) = \emptyset$)
I think the proving should go that I suppose that it is possible, and somehow I have to get contradiction, but I have no idea how. :)
Edit: Answer found, thanks for help!
The answer comes directly from Baire's category theorem, which mentions an (X,d) metric space, and if it is not the empty set, and it is a complete metric space, then the statement is true for it, and obviously $\mathbb{R}$ is a complete metric space.