The most accurate response regarding what it means for a set to be "closed" is: An operation performed on members of that set will result in a member of the same set.
In mathematical terms, a set is considered closed under a particular operation (such as addition, multiplication, etc.) if performing that operation on members of the set always produces a result that is also a member of the set. For example, the set of integers is closed under addition because the sum of any two integers is also an integer.