1)$A^o$ 2)$\overline A$ 3)$A'$ in $A=(-\infty,0)\cap Q$

Question

so in R with the classic metric so d(x,y) = |x-y| and for $A=(-\infty,0)\cap Q$ I have to find 1)$A^o$ which is the interior of A 2)$\overline A$ 3)$A'$

1. I believe $A^o=\emptyset$ because for every $x \in A$ $B(x,e)$ with $e > 0$ isnt a part of A
2. Easily proven $\overline A =A\cup {0}$
3. I believe $A^o=\emptyset$ similar with 1)

Any thoughts on these?

Answer 1

Your answer for 1. is correct but $\overline A=(-\infty, 0]$ and $A'=(-\infty, 0]$. Every point of $(-\infty, 0]$ is a limit point of $A$.