A set $M \subseteq \mathbb{R}$ is called open if $\mathbb{R} \setminus M$ is closed. How do you prove that $(2n -1/2, 2n + 1/2)$ is open?
I‘m confused because it means $2n - 1/2 < 2n + 1/2$ but how can I write it as a complement?
In this case, these are all numbers outside the interval $(2n - 1/2, 2n + 1/2)$. Is it then $[-\infty, 2n-1/2)$ and $(2n+1/2, +\infty]$?
$$\mathbb{R}\setminus{(2n-1/2, 2n+1/2)}=(-\infty,2n-1/2]\cup[2n+1/2,+\infty),$$ which is the union of two closed sets (in the standard topology)