Prove that the Interior of the Boundary is Empty Suppose X is a Metric Space
Let S $\subset X$
Prove that if S is Closed then, the Interior of the Boundary of S is Empty
Totally stuck on how to solve this.

Note that  $int(\partial A)=int(cl(A) \setminus int(A))$, then we have $int(cl(A)\setminus int(A))=cl(A) \setminus cl(int(A))$. Since $int(A) \subset A $, thus $cl(int(A)) \subset cl(A))$. Hence $cl(A) \setminus cl(int(A)) = \emptyset $. Therefore $int(\partial A)=\emptyset$.
