support

Support

The support of an object (function/set/distribution/…) is the region where it is “present” or non-zero.
Outside the support, the object vanishes or is undefined in the given context.

Let $f:X\to A$ and suppose $A$ has a distinguished “zero” element $0$.
The support of $f$ is:

$$\text{supp }f=\{x\in X\mid f(x)\ne 0\}$$