complex-valued continuous functions with compact support on H-lc

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

Definition 1.1   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}$.

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



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