Closed ideals in the functionally countable subalgebra of C(X)

In this paper, closed ideals in Cc(X), the functionally countable subalgebra of C(X), with mc-topology, is studied. We show that ifX CUC-space, then C*c(X) uniform norm-topology a Banach algebra. Closed Cc(X) as modified analogue C(X) m-topology are characterized. For zero-dimensional space X, we proper ideal if and only it an intersection maximal Cc(X). It also shown every mc-topology X P-space closed. Moreover, for strongly proved properly pseudo compact. Finally, F ec-filter on ec-ultrafilter zc-ultrafilter.