A set is called closed under an operation if applying an operation on elements of a set always leads to an element of that set. But what about the opposite, when an operation on an element of the set never leads to an element of the set? Is there also a name for that?
Examples:
The set of even numbers is closed under multiplication: The product of even numbers always is even.
The set of primes is ??? under multiplication: The product of primes is never a prime.
The set of single-digit numbers is neither closed nor ??? under multiplication: The product of two single-digit numbers may or may not be a single-digit number.
The set of integers is closed under negation: The negation of an integer is always an integer.
The set of positive numbers is ??? under negation: The negation of a positive number is never positive.
The set of non-negative integers is neither closed nor ??? under negation: The negation of a non-negative number may or may not be non-negative.
