Definition 5.19.2 (Compactly Supported).label Let $X$ be a topological space, $E$ be a TVS over $K \in \RC$, and $f \in C(X; E)$, then $f$ is compactly supported if $\supp{f}$ is compact. The set $C_{c}(X; E)$ is the vector space of all $E$-valued compactly supported functions on $X$.