Definition:Strict Up-Set

Remark
In most cases, there can be no confusion as to whether the strict up-set of an element or of a set is intended. Where that is ambiguous, it should be indicated in the text.

Also known as
Some call this a strict up set or strict upper set.

Some place the arrow after the element instead of before.

Some use $U(a)$ instead of ${\dot\uparrow} a$.

On, this is often called strict upper closure and written ${\uparrow}a$, but this is changing.

Also see

 * Strict Down-Set
 * Upper Closure