# Definition:Characteristic Function (Set Theory)/Set/Support

## Definition

Let $S$ be a set

Let $E \subseteq S$ be a subset.

Let $\chi_E: S \to \left\{{0, 1}\right\}$ be the characteristic function of $E$.

The support of $\chi_E$, denoted $\operatorname{supp} \chi_E$, is the set $E$. That is:

$\operatorname{supp} \chi_E = \left\{{x \in S: \chi_E \left({x}\right) = 1}\right\}$