ec-Filters and ec-ideals in the functionally countable subalgebra of C*(X)

[EN] The purpose of this article is to study and investigate ec-filters on X and ec-ideals in Cc (X) in which they are in fact the counterparts of zc-filters on X and zc-ideals in Cc(X) respectively. We show that the maximal ideals of Cc (X) are in one-to-one correspondence with the ec-ultrafilters on X. In addition, the sets of ec-ultrafilters and zc-ultrafilters are in one-to-one correspondence. It is also shown that the sets of maximal ideals of Cc(X) and Cc (X) have the same cardinality. As another application of the new concepts, we characterized maximal ideals of Cc (X). Finally, we show that whether the space X is compact, a proper ideal I of Cc(X) is an ec-ideal if and only if it is a closed ideal in Cc(X) if and only if it is an intersection of maximal ideals of Cc(X).