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 $f$:
 * $\map \supp f = \cl {\set {x \in X: \map f x \ne e} }$

Also see

 * Definition:Support of Mapping to Algebraic Structure