\begin{definition}[Definition:Characteristic Function (Set Theory)/Set/Support]
Let $S$ be a set
Let $E \subseteq S$ be a subset.
Let $\chi_E: S \to \set {0, 1}$ be the characteristic function of $E$.
The '''support''' of $\chi_E$, denoted $\supp \chi_E$, is the set $E$.
That is:
:$\supp \chi_E = \set {x \in S: \map {\chi_E} x = 1}$
\end{definition}