Definition 0.1. $C_c\left(G\right)$ is defined as the class of continuous functions acting on a topological groupoid $G$ with compact support, and with values in a normed space, field,, or algebraic structure. In most applications it will, however, suffice to select $G$ as a locally compact (topological) groupoid, $G_{\mathit{lc}}$, support for this space of continuous functions.