Can a closed set in $\Bbb R$ be written in terms of open sets Is it possible to write any non-empty closed set in $\Bbb R$ as a combination of unions / intersection of open sets. Note that I don't demand just one union / intersection. I am happy with any combination (finite) of unions / intersection, but elements in each union/intersection must be open set. Any finite set, closed interval, cantor set can be written like this. 

Let $[a,b]\subset\mathbb{R}$ be a closed set then you can write $[a,b]=\cap_n(a-\frac{1}{n},b+\frac{1}{n})$ as $n\to\infty$.
