Let $R \subseteq X \times Y$
Is there a commonly used term/notation for the functions $f:X\rightarrow \mathcal{P}(Y)$ and $g:Y\rightarrow \mathcal{P}(X)$ defined as follows?:
$$f(x) = \{ y \mid (x, y) \in R\}$$ $$g(y) = \{ x \mid (x, y) \in R\}$$
Since these values are a very elementary part of the structure of a relation, I'd think that this shows up commonly and might have a name.
If there is notation for $f$ then perhaps $g$ doesn't need different notation as $g$ is just $f$ on $R^{-1}$