How do i prove that this given set is open? Let $X$ be a topological space and $E$ be an open set.
If $A$ is open in $\overline{E}$ and $A\subset E$, then how do i prove that $A$ is open in $X$?
It seems trivial, but i'm stuck.. Thank you in advance.

Is enough to show that $A=G\cap E$ for an open set $G\subset X$.
Use the hypothesis and the fact that $A=G\cap \overline{E}\Rightarrow A=G\cap E$  (why?).
