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

Definition
Let $E \subseteq S$.

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 $E$, or, more generally:


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

Also see

 * Definition:Support