PlanetPhysics/CCG

Class of continuous functions on a topological groupoid with compact support

Def. $C_c(𝖦)$ is defined as the class of continuous functions [1] 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, ${𝖦}_{lc}$, support for this space of continuous functions.

Note: this concept is important for quantum theoretical applications related to quantum groupoids defined by a $C_c(𝖦)$.