Prove that $\overline{\mathrm{Int}\,(\overline{\mathrm{Int}\,A})} = \overline{\mathrm{Int}\,A}$ I need to proof this statement, and I don't know where to start.
In every topological sapce, we have that $\overline{\mathrm{Int}\,(\overline{\mathrm{Int}\,A})} = \overline{\mathrm{Int}\,A}$
I tried to show that $\mathrm{Int}\,(\overline{\mathrm{Int}\,A})$ is closed, but I don't know how.
Thanks!

Hint: One inclusion is fairly straightforward (use $\operatorname{Int}B \subseteq B$). For the other, show that $\operatorname{Int}A \subseteq \operatorname{Int}(\overline{\operatorname{Int}A})$.
