Suppose $A$ and $B$ are (complete) ordered sets. Suppose $R\subseteq A\times B$, and


$f(a)=\inf\{b : (a,b)\in R\}$


$g(b)=\inf\{a : (a,b)\in R\}$


then what can we call $f$ and $g$? Perhaps there is some standard terminology.



Uniformizing a relation on ordered sets
The maps $f,g$ constitute a Galois connection, but you have to take $\leq := \supseteq$ in both cases.


