# 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 ${\displaystyle H-{lc}}$.}

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

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