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. Perhaps words like "envelope" or "transpose" could be involved? If it helps, assume $A=B=\mathbb N$.

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.