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%%% Primary Title: C-cG
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%%% Owner: bci1
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\begin{document}
\subsection{Class of continuous functions on a topological groupoid with compact support}
\begin{definition} $C_c(\mathsf{G})$ is defined as the
\emph{class of continuous \htmladdnormallink{functions}{http://planetphysics.us/encyclopedia/Bijective.html} acting on a \htmladdnormallink{topological groupoid}{http://planetphysics.us/encyclopedia/EquivalenceRelation.html} $\mathsf{G}$ with compact support, and with values in a normed space, \htmladdnormallink{field}{http://planetphysics.us/encyclopedia/CosmologicalConstant2.html},}, or \htmladdnormallink{algebraic structure}{http://planetphysics.us/encyclopedia/TrivialGroupoid.html}. 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.
\end{definition}
\textbf{Note:}
this \htmladdnormallink{concept}{http://planetphysics.us/encyclopedia/PreciseIdea.html} is important for quantum theoretical applications related to \htmladdnormallink{quantum groupoids}{http://planetphysics.us/encyclopedia/WeakHopfAlgebra.html} defined by a $C_c(\mathsf{G})$.
\end{document}
