[[Analysis MOC]]
# Support of a map

The **support** $\mathrm{supp}(f)$ of a real-valued function $f: X \to\mathbb{R}$ is the set of all $x \in X$ mapped to zero, #m/def/anal 
i.e.
$$
\begin{align*}
\mathrm{supp}(f) = \{ x \in X : f(x) \neq 0 \}
\end{align*}
$$
if $X$ is a [[topological space]] the **closed support** $\mathrm{clsupp}(f)$, also called the **support** is the [[closure]] of the support defined above.

## Further terminology

- A function is said to have **compact support** iff the closed support is [[Compact space|compact]].

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#state/tidy | #lang/en | #SemBr