A set is generated from the set of real numbers R to contain all points in R, all open, semi-open, and closed intervals in R. Additionally, this set contains all other sets generated by a countable number of set operations including complementation, intersection, and union. This set is referred to as a Borel field, which is the same on R as the power set. a Vitali set. a Borel field on R. a power set of R