Definition:Support of Continuous Mapping

General topological group
Let $X$ be a topological space.

Let $G$ be a topological group with identity $e$.

Let $f : X \to G$ be a continuous mapping.

The support of $f$ is the closure of the set of elements of $X$ that do not map to $e$ under $f$:
 * $\operatorname{supp} \left({f}\right) = \overline{\left\{{x \in X: f \left({x}\right) \ne e}\right\}}$

Also see

 * Definition:Support of Mapping to Algebraic Structure