Is the boundary of a finite subset of $\mathbb{R}$ just that same subset once again, and if so how does this mesh with the definition of small/large inductive dimension for the topology on $\mathbb{R}$?
If $Bd(X)=\overline{X}\setminus intX$ and finite subsets of $\mathbb{R}$ are closed with empty interior this seems to be the case, but then the definition for the small inductive dimension of a point fails to yield dimension $0$ since the boundary of the point is itself and not the empty set. Any help is appreciated.