I have this problem:
let $Y$ be a closed subspace in $X$. If $A\subset X$ and $H$ is an open neighborhood of $Y\cap A$ in $Y$. Prove that $A\cap (\overline{Y\setminus H}) = \emptyset$. ($\overline{Y\setminus H}$) is the closure of $Y \setminus H$ in $X$.
I don´t see why it works, neither how to prove it, I hope someone can help me! Thank you