$\varkappa_{y} \in \Pi_{X} \, \{ 0, \, 1 \}$, so $\varkappa_{y} : X \to \{ 0, \, 1 \}$ defined as:
$$\varkappa_{y}(x) = \begin{cases}
1, & \text{if}\ x \in Y\\ 0, & \text{if}\ x \notin Y
\end{cases}$$