Definition:Supremum/Also known as

Definition
Particularly in the field of analysis, the supremum of a set $T$ is often referred to as the least upper bound of $T$ and denoted $\map {\operatorname {lub} } T$ or $\map {\operatorname {l.u.b.} } T$.

Some sources refer to the supremum of a set as the supremum on a set.

Some sources introduce the notation $\displaystyle \sup_{y \mathop \in S} y$, which may improve clarity in some circumstances.