… addition.

A set is closed under_addition_if you can add any two numbers in the set and still have a number in the set as a result.

… (scalar) multiplication.

A set is closed under (scalar)_multiplication_if you can multiply any two elements, and the result is still a number in the set.


Generally, β€œclosed under_some operation_” means the elements of the set are not being able to β€œescape” the set using that operation. The result always the set they are from.