Consider the topological space $\mathbb{R}$ equipped with the standard topology. Determine the interior, closure and boundary of this set and decide whether it is open or closed:
$a \in \mathbb R: K_a = \{ \frac{a}{n+m} | n, m \in \mathbb N_+ \} $
So, I know that all of the elements of this set lie somewhere in the intervall $]0; \frac a 2]$ for $ a > 0$ or in $]\frac a 2; 0]$ for $a < 0$. I also know, that the elements are not continuous, i.e. it is a pointwise set. But at this point I am finished and do not know, how to carry on:
I don't understand how I can determine the 3 properties of the set (interior, closure and boundary), when the set is made of numbers that are not neighboring (if you understand what I mean)