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 $$C_c (H_{lc)$$} 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 $$X = H_{lc}$$.