When $T$ is the set of natural numbers with usual Euclidean metric (equivalent to discrete metric on $\mathbb{N}$) then $C(T) =l^{\infty}, C_0(T) = c_0, C_c(T) = c_{00}$, where $C(T), C_0(T), C_c(T) $ means continuous function on $T$, continuous function vanishing at zero, continuous function with compact support respectively.
How can I identify?I tried but not getting any clue. Please help.