a note on c(x) as an l_{cc}(x)-module

Let $ l_{cc}(x)=lbrace f in c(x) : vert xsetminus c_{f}vert leq aleph_{0} rbrace$, where $ c_{f} $ is the union of all open subsets $ usubseteq x $ such that $ vert f(u)vert leq aleph_{0} $.we introduce and study $c(x)$ as an $l_{cc}(x)$-module.it is shown that whenever $x$ be a $lcc$-completely regular space, then $l_{cc}(x)$-module $c(x)$ is finitely generated if and only if $c(x)=l_{cc}(x)$.