Definition:Supremum of Mapping/Real-Valued Function

Definition
Let $f: S \to \R$ be a real-valued function.

Let $f$ be bounded above on $S$.

Also see

 * Continuum Property, which guarantees that this supremum always exists.


 * Equivalence of Definitions of Supremum of Real-Valued Function


 * Definition:Infimum of Real-Valued Function


 * Definition:Supremum of Mapping
 * Definition:Infimum of Mapping