0
$\begingroup$

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

  • 0
    Can you give some background information about how you run into this problem? Also, what do you mean by 'Y be a closed subspace of X'? Subspace in the linear sense or just a subset with topology induced from $X$?2012-09-19
  • 0
    @Hui Yu: This is clearly just topology.2012-09-19
  • 0
    @BrianM.Scott Yes. I got confused because I am now studying topological vector spaces.2012-09-19

1 Answers 1