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. 

All the answers seems to be considering countable operations, but you ask for finite unions and intersections as I read it. Then, the answer is no. To see this, just note that finite intersections of open sets are open and the union of any number of open sets is also open. Thus, if you are only allowed to use finite intersections and unions, you can only ever hope to construct open sets from open sets.
