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 [[../LocallyCompactHausdorffSpaces/|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 [[../Bijective/|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 [[../CoIntersections/|topological]] space $X=H_{lc}$.