PlanetPhysics/Complex Valued Continuous Functions With Compact Support on Hlc

\section{Class of complex-valued continuous functions with compact support on a a locally compact Hausdorff space $H-{lc}$.}

Let $H_{lc}$ be a locally compact Hausdorff space. Then, one defines the notation Failed to parse (syntax error): {\displaystyle C_c (H_{lc)} } as the space of complex-valued continuous functions with compact support on $H_{lc}$.

{\mathbf Note:} For simplicity, this is also denoted as $C_{c}(X)$ even though it is tacitly assumed that the topological space $X=H_{lc}$.