Is there a name for constructing a set from a relation (or, more generally speaking, from a set of pairs that are tuples)? For example, let $R = \{(0, 1), (1, 2), (2, 3)\}$; if you collect all the second elements in the tuples (pairs) you get $A = \{1, 2, 3\}$.
Is there a name for the subset of a relation for which the first element in each list is a certain $x$? This means that there is some sort of filter operation $f(x, R)$ that gives you R', where R' is the subset of $R$ with all the pairs in R' having $x$ as its first element.
Thanks.