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

That is:

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

Also see

• Definition:Fiber of Truth

Sources

• 2008: Paul Halmos and Steven Givant: Introduction to Boolean Algebras ... (previous) ... (next): $\S 3$
• 2008: Paul Halmos and Steven Givant: Introduction to Boolean Algebras ... (previous) ... (next): Appendix $\text{A}$: Set Theory: Cantor's Theorem