Yes. Furthermore, consider any set of finitely many points in R. It will be a closed set and have empty interior, so the formula will fail .
That if D is a closed set then D = Cl(Int(D)) where Cl and Int denote closure and interior. I don't think it's true though. Counter example:
Let .
D is closed, since it is the union of two closed sets, and Int(D) = (1,2). Therefore Cl(Int(D)) = Cl(1,2) = [1,2], which is a proper subset of D.
Is this correct?