C-cG

Class of continuous functions on a topological groupoid with compact support

Definition 0.1   $ C_c(\mathsf{G})$ is defined as the class of continuous functions 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})$ .



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