Let $X$ be a D11: Set.
The indicator function on $X$ with respect to $E \subseteq X$ is the D992: Function
\begin{equation}
X \to \{ 0, 1 \}, \quad
x \mapsto
\begin{cases}
1, \quad & x \in E \\
0, \quad & x \in X \setminus E
\end{cases}
\end{equation}