Definition:Support

Discussion
The support of a mapping can have different meanings depending on the properties of the mapping under consideration.

Real-Valued Function on an Abstract Set
Let $f: S \to \R$ be a real-valued function.

The support of $f$ is the set of elements $x$ of $S$ whose values under $f$ are non-zero.

That is:
 * $\operatorname{supp} \left({f}\right) = \left\{{x \in S: f \left({x}\right) \ne 0}\right\}$

Continuous Real-Valued Function in $\R^n$
Let $f: \R^n \to \R$ be a continuous real-valued function.

The support of $f$ is the closure of the set of elements $x$ of $\R^n$ whose values under $f$ are non-zero.

That is:
 * $\operatorname{supp} \left({f}\right) = \overline{\left\{{x \in \R^n: f \left({x}\right) \ne 0}\right\}}$