I need to find the interior, accumulation points, closure, and boundary of the set
$ A = \left\{ \frac1n + \frac1k \in \mathbb{R} \mid n,k \in \mathbb{N} \right\} $ and use the information to determine whether the set is bounded, closed, or compact.
So far, I have that the interior is empty, but not sure how to prove it. My thoughts are to fix $n$ and then the accumulation points would be $\left\{ \frac 1n \mid n \in \mathbb{N} \right\}$. But I'm not sure if that is correct. Then, I believe that the boundary is $[0,2]$. Can someone confirm that?
Any help would be appreciated.