Definition:Characteristic Function (Set Theory)/Set/Support
< Definition:Characteristic Function (Set Theory) | Set(Redirected from Definition:Support of Characteristic Function)
Jump to navigation
Jump to search
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 $\supp \chi_E$, is the set $E$.
That is:
- $\supp \chi_E = \set {x \in S: \map {\chi_E} x = 1}$
Also see
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