A is closed in X$\Longleftrightarrow$ $\partial(A)\subset A$ I would like to prove that
let A a subset of a metric space
A is closed in X $\Longleftarrow$ $\partial(A)\subset A$
Please I need a suggestion.
I tried to prove that $A^´\subset A$...

Let $\overline{A}$ denote the closure of $A$.
If $A$ is closed, $A=\overline{A}$. Hence, $\partial{A}=\overline{A}\cap X\backslash intA=A\cap X\backslash intA\subseteq A$.
Note, $\overline{A}=A\cup \partial{A}$. Thus if $\partial{A}\subseteq A$, then $\overline{A}\subseteq A$.
