The property $∀x:x≤f(x)$ is also called „extensional“, especially with respect to closure systems or lattices.

In general, a closure system is defined as the image of a closure operator, which is an idempotent and extensional endomorphism of an ordered set.

The property $∀x:x≤f(x)$ is also called „extensive“, especially with respect to closure systems or lattices.

In general, a closure system is defined as the image of a closure operator, which is an idempotent and extensional endomorphism of an ordered set.