a class is a collection of sets with a shared property
a class of sets is called
- -closed (closed under intersections) or a -system if whenever ,
- -closed (closed under countable intersections) if for any choice of countably many sets ,
- -closed (closed under unions) if whenever ,
- -closed (closed under countable unions) if for any choice of countably many sets ,
- -closed (closed under differences) if whenever , and
- closed under complements if for any set .