stylistic:tone, information:classification, quality:correction, stylistic:style_transfer, structural:reformatting
Exact upper bounds

An upper bound u of a subset S of a preordered set (K, ≤) is said to be an exact upper bound for S if every element of K that is strictly majorized by u is also majorized by some element of S. Exact upper bounds of reduced products of linear orders play an important role in PCF theory.