PlanetPhysics/CCG

Class of continuous functions on a topological groupoid with compact support

Def. $C_{c}({\mathsf {G}})$ is defined as the class of continuous functions [1] acting on a topological groupoid ${\mathsf {G}}$ with compact support, and with values in a normed space, field, or algebraic structure. In most applications it will, however, suffice to select ${\mathsf {G}}$ as a locally compact (topological) groupoid, ${\mathsf {G}}_{lc}$, support for this space of continuous functions.

Note: this concept is important for quantum theoretical applications related to quantum groupoids defined by a $C_{c}({\mathsf {G}})$.