A Borel set is an element of a Borel sigma-algebra. Roughly speaking, Borel sets are the sets that can be constructed from open or closed sets by repeatedly taking countable unions and intersections. Formally, the class of Borel sets in Euclidean is the smallest collection of sets that includes the open and closed sets such that if , , , ... are in , then so are , , and , where is a set difference (Croft et al. 1991).
The set of rational numbers is a Borel set, as is the Cantor set.