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 $\displaystyle D = {0} \cup [1,2] $.

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?