Dominance

The dominance Relation on a Set of points in Euclidean $n$-space is the Intersection of the $n$ coordinate-wise orderings. A point $p$ dominates a point $q$ provided that every coordinate of $p$ is at least as large as the corresponding coordinate of $q$.

The dominance orders in $\Bbb{R}^n$ are precisely the Posets of Dimension at most $n$.

See also Partially Ordered Set, Realizer