A set is closed under an operation if performing that operation on the members of that set always produces a member of that set.
For example, the whole numbers Z = { ..., -3 , -2, -1 , 0 , 1 , 2 , 3, ...} are closed under addition.
It doesn't matter what pair of numbers are added, the result will always be a whole number.
It is true for subtraction and multiplication too, but not under division.
The division of 4/2 = 2 gives a whole number, but 7/3 is not a whole number, thus the set of the whole numbers is not closed under division.
The only set, with enough amplitude to be closed under all four operations, is the set of the real numbers, with the sole exception of the number 0.
We cannot divide by 0.
If a set of numbers was to be given as valid for all four basic operations is the set of the real number except the 0. R - {0}