4
$\begingroup$

Let $D$ be a dense in $X$. Prove that for every open set $U\subseteq X$, $$\newcommand{\cl}{\operatorname{cl}}\cl (D \cap U) = \cl(U)$$

For my solution, what I did is by showing that the $\cl(D \cap U)$ is contained in $\cl(U)$ and vice versa.

I've done the $\subseteq$. I have trouble in the $\supseteq$ part.

or is their an easier solution where I don't need the inclusions?

  • 0
    I have added a `\cl` command to be available on this page.2012-11-19

2 Answers 2