Consider the set $[a,\infty)$ where a is a real number. Then this is not open since $a$ is included.The complement of the set is $(-\infty,a)$, which is open, so it is a closed set. Is this correct? Also, for $\frac{1}{n}$ where $n$ is a positive integer. The set is in the interval $(0,1]$. This is not open, but I don't think it's closed either since the complement is $(-\infty,0]\cup(1,\infty)$.
Any feedback is appreciated, thanks.