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

This page is about Support in the context of characteristic Function in set theory. For other uses, see Support.

## Definition

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 $\operatorname{supp} \chi_E$, is the set $E$.

That is:

$\operatorname{supp} \chi_E = \set {x \in S: \map {\chi_E} x = 1}$