That K is a relation between X and Y means it is a subset of the Cartesian product \\(X \times Y\\).

Let \\(f_1: X \rightarrow 2^Y\\) be the function sending an object \\(o \in X\\) to the set of attributes which apply to \\(o\\), i.e.,

\\[f_1(o) = \lbrace a \in Y\ |\ (o,a) \in K \rbrace \\]

I called it \\(f_1\\) because it operates on a single object.

Let \\(f_1: X \rightarrow 2^Y\\) be the function sending an object \\(o \in X\\) to the set of attributes which apply to \\(o\\), i.e.,

\\[f_1(o) = \lbrace a \in Y\ |\ (o,a) \in K \rbrace \\]

I called it \\(f_1\\) because it operates on a single object.